Maths-
General
Easy

Question

Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...

Hint:

  • A sequence is said to be arithmetic if the common difference is always constant.
  • The General formula of any AP is a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d.

The correct answer is: ⇒-7


    Explanation:
    • We have given a sequence 93,86,79,72,66,....
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 93,86,79,72,66,....
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 86 minus 93 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 79 minus 86 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 72 minus 79 end cell row cell not stretchy rightwards double arrow negative 7 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.

    Related Questions to study

    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 2 x plus 6 space straight & space y equals 1 half x plus 3

    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

     y equals 2 x plus 6

    y equals 1 half x plus 3
    Slope of both lines are 2,1 half respectively
    Since slope are not equal then both are not parallel.
    Product of both slope is 2 cross times 1 half equals 1
    So, both are not perpendicular also.
    So,
    Both are nor parallel neither perpendicular.

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 2 x plus 6 space straight & space y equals 1 half x plus 3

    Maths-General
    • We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
    Step 1 of 1:
    We have given two equations

     y equals 2 x plus 6

    y equals 1 half x plus 3
    Slope of both lines are 2,1 half respectively
    Since slope are not equal then both are not parallel.
    Product of both slope is 2 cross times 1 half equals 1
    So, both are not perpendicular also.
    So,
    Both are nor parallel neither perpendicular.

    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...

    • We have given a sequence 37,34,31,29,26,23,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 37,34,31,29,26,23,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 34 minus 37 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 31 minus 34 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 29 minus 31 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...

    Maths-General
    • We have given a sequence 37,34,31,29,26,23,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 37,34,31,29,26,23,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 34 minus 37 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 31 minus 34 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 29 minus 31 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    General
    Maths-

    What are the horizontal asymptotes for the graph
    f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction

    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x - value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 + 7x + 12 = 0
    x2 + 3x + 4x + 12 = 0
    x(x + 3) + 4(x + 3) = 0
    (x + 3) (x + 4) = 0
    x = -3   or   x = -4
    The vertical asymptote of the rational function is x =−3 and x = -4
    This function has x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x = -3 and x = -4.

    What are the horizontal asymptotes for the graph
    f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction

    Maths-General
    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x - value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 + 7x + 12 = 0
    x2 + 3x + 4x + 12 = 0
    x(x + 3) + 4(x + 3) = 0
    (x + 3) (x + 4) = 0
    x = -3   or   x = -4
    The vertical asymptote of the rational function is x =−3 and x = -4
    This function has x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x = -3 and x = -4.
    parallel
    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

    • We have given a sequence 3,6,9,15,18,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 3,6,9,15,18,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 6 minus 3 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 9 minus 6 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 15 minus 9 end cell row cell not stretchy rightwards double arrow 6 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

    Maths-General
    • We have given a sequence 3,6,9,15,18,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 3,6,9,15,18,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 6 minus 3 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 9 minus 6 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 15 minus 9 end cell row cell not stretchy rightwards double arrow 6 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.

    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

    • We have given a sequence 3,6,9,12,15,18,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 3,6,9,12,15,18,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 6 minus 3 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 9 minus 6 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 12 minus 9 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

    Maths-General
    • We have given a sequence 3,6,9,12,15,18,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 3,6,9,12,15,18,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 6 minus 3 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 9 minus 6 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 12 minus 9 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...

    • We have given a sequence 1 comma negative 2 comma 3 comma negative 4 comma 5
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 1 comma negative 2 comma 3 comma negative 4 comma 5
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow negative 2 minus 1 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 3 minus left parenthesis negative 2 right parenthesis end cell row cell not stretchy rightwards double arrow 5 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow negative 4 minus 3 end cell row cell not stretchy rightwards double arrow negative 7 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...

    Maths-General
    • We have given a sequence 1 comma negative 2 comma 3 comma negative 4 comma 5
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 1 comma negative 2 comma 3 comma negative 4 comma 5
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow negative 2 minus 1 end cell row cell not stretchy rightwards double arrow negative 3 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 3 minus left parenthesis negative 2 right parenthesis end cell row cell not stretchy rightwards double arrow 5 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow negative 4 minus 3 end cell row cell not stretchy rightwards double arrow negative 7 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.

    parallel
    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...

    • We have given a sequence 77,64,51,38,25,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 77,64,51,38,25,..
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 64 minus 77 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 51 minus 64 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 38 minus 51 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...

    Maths-General
    • We have given a sequence 77,64,51,38,25,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 77,64,51,38,25,..
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 64 minus 77 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 51 minus 64 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 38 minus 51 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....

    • We have given a sequence 1,15,29,43,57,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 1,15,29,43,57,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 15 minus 1 end cell row cell not stretchy rightwards double arrow 14 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 29 minus 15 end cell row cell not stretchy rightwards double arrow 14 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 43 minus 29 end cell row cell not stretchy rightwards double arrow 14 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....

    Maths-General
    • We have given a sequence 1,15,29,43,57,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 1,15,29,43,57,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 15 minus 1 end cell row cell not stretchy rightwards double arrow 14 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 29 minus 15 end cell row cell not stretchy rightwards double arrow 14 end cell end table
    Then, The difference between next two terms will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 43 minus 29 end cell row cell not stretchy rightwards double arrow 14 end cell end table
    Since the difference is constant
    The given sequence is an arithmetic sequence.

    General
    Maths-

    Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....

    • We have given a sequence 47,39,31,23,15,...
    • We have to find the recursive formula.
    Step 1 of 1:
    We have given a sequence 47, 39, 31, 23, 15, ....
    The given sequence is an AP.
    We know that the recursive formula for any AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here the common difference is - 8
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript plus d

    a subscript n equals a subscript n minus 1 end subscript minus 8

    Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....

    Maths-General
    • We have given a sequence 47,39,31,23,15,...
    • We have to find the recursive formula.
    Step 1 of 1:
    We have given a sequence 47, 39, 31, 23, 15, ....
    The given sequence is an AP.
    We know that the recursive formula for any AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here the common difference is - 8
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript plus d

    a subscript n equals a subscript n minus 1 end subscript minus 8

    parallel
    General
    Maths-

    Write a recursive formula for the given sequence. 81,85,89,93,97,....

    Explanation:
    • We have given a sequence 81,85,89,93,97,...
    • We have to find the recursive formula.
    Step 1 of 1:
    We have given a sequence 81,85,89,93,97,...
    The given sequence is an AP.
    We know that the recursive formula for any AP is a subscript n equals a subscript n minus 1 end subscript plus d , where d is common difference.
    Here the common difference is 4
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript plus d
    a subscript n equals a subscript n minus 1 end subscript plus 4

    Write a recursive formula for the given sequence. 81,85,89,93,97,....

    Maths-General
    Explanation:
    • We have given a sequence 81,85,89,93,97,...
    • We have to find the recursive formula.
    Step 1 of 1:
    We have given a sequence 81,85,89,93,97,...
    The given sequence is an AP.
    We know that the recursive formula for any AP is a subscript n equals a subscript n minus 1 end subscript plus d , where d is common difference.
    Here the common difference is 4
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript plus d
    a subscript n equals a subscript n minus 1 end subscript plus 4

    General
    Maths-

    Write a recursive formula for the given sequence. 81,85,89,93,97,....

    Explanation:
    • We have given a sequence 4,7,10,14,..
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 4,7,10,14,...
    The difference in first two terms is
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 7 minus 4 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Now the difference in next two terms is
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 10 minus 7 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Then, The difference between next two terms will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 14 minus 10 end cell row cell not stretchy rightwards double arrow 4 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.

    Write a recursive formula for the given sequence. 81,85,89,93,97,....

    Maths-General
    Explanation:
    • We have given a sequence 4,7,10,14,..
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 4,7,10,14,...
    The difference in first two terms is
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 7 minus 4 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Now the difference in next two terms is
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 10 minus 7 end cell row cell not stretchy rightwards double arrow 3 end cell end table
    Then, The difference between next two terms will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 14 minus 10 end cell row cell not stretchy rightwards double arrow 4 end cell end table
    Since the difference is not constant
    The given sequence is not an arithmetic sequence.
    General
    Maths-

    How do you find vertical and horizontal asymptotes of a rational function?
    What are the vertical asymptotes for the graph of f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction

    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 +7x + 12 = 0
    x2 + 3x + 4x + 12 = 0
    x(x + 3) + 4 (x + 3) = 0
    (x + 3)(x + 4)=0
    x= -3  or  x = -4
    The vertical asymptote of the rational function is x=−3 and x=-4
    This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= -3 and x = -4.

    How do you find vertical and horizontal asymptotes of a rational function?
    What are the vertical asymptotes for the graph of f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction

    Maths-General
    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 +7x + 12 = 0
    x2 + 3x + 4x + 12 = 0
    x(x + 3) + 4 (x + 3) = 0
    (x + 3)(x + 4)=0
    x= -3  or  x = -4
    The vertical asymptote of the rational function is x=−3 and x=-4
    This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= -3 and x = -4.
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    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

    • We have given a sequence 15,13,11,9,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 15,13,11,9,...
    The difference in first two terms is
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 13 minus 15 end cell row cell not stretchy rightwards double arrow negative 2 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 11 minus 13 end cell row cell not stretchy rightwards double arrow negative 2 end cell end table
    Since the difference is constant
    The given sequence is arithmetic sequence.

    Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

    Maths-General
    • We have given a sequence 15,13,11,9,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 15,13,11,9,...
    The difference in first two terms is
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 13 minus 15 end cell row cell not stretchy rightwards double arrow negative 2 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 11 minus 13 end cell row cell not stretchy rightwards double arrow negative 2 end cell end table
    Since the difference is constant
    The given sequence is arithmetic sequence.

    General
    Maths-

    Write an explicit formula for the arithmetic sequence.
    an = 12 - 5n

    • We have given an explicit formula an = 12 - 5n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 12 - 5n

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 12 minus 5 end cell row cell a subscript 1 equals 7 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 12 minus 5 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 12 minus 5 n plus 5 end cell row cell a subscript n minus 1 end subscript equals a subscript n plus 5 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n plus 5.

    Write an explicit formula for the arithmetic sequence.
    an = 12 - 5n

    Maths-General
    • We have given an explicit formula an = 12 - 5n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 12 - 5n

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 12 minus 5 end cell row cell a subscript 1 equals 7 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 12 minus 5 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 12 minus 5 n plus 5 end cell row cell a subscript n minus 1 end subscript equals a subscript n plus 5 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n plus 5.

    General
    Maths-

    Write an explicit formula for the arithmetic sequence.
    an = 8 + 3n

    • We have given an explicit formula an = 8 + 3n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 8 + 3n
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 8 plus 3 end cell row cell a subscript 1 equals 11 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 8 plus 3 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 8 plus 3 n minus 3 end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 3 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n minus 3.

    Write an explicit formula for the arithmetic sequence.
    an = 8 + 3n

    Maths-General
    • We have given an explicit formula an = 8 + 3n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 8 + 3n
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 8 plus 3 end cell row cell a subscript 1 equals 11 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 8 plus 3 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 8 plus 3 n minus 3 end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 3 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n minus 3.

    parallel

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