Maths-
General
Easy

Question

Write recursive formula and find the first term. a subscript n equals 108 minus n

Hint:

  • Recursive Formula is a formula that defines the each term of sequence using the previous/preceding terms.

The correct answer is: a_(n-1)=a_n+1.


    Explanation:
    • We have given a explicit function a subscript n equals 108 minus n.
    • We have to find the recursive formula and first term.
    Step 1 of 2:
    We have given explicit formula a subscript n equals 108 minus n.
    First term 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 a subscript n equals 108 minus n end cell row cell a subscript 1 equals 108 minus left parenthesis 1 right parenthesis end cell row cell a subscript 1 equals 107 end cell end table
    Step 2 of 2:
    Now for recursive formula we will calculate an-1.
    So,

    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 108 minus left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 108 minus n plus 1 end cell row cell a subscript n minus 1 end subscript equals a subscript n plus 1 end cell end table
    .

    Related Questions to study

    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 4 x plus 1 space straight & space y equals negative 4 x minus 2

    • 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 = 4x + 1
    y = -4x - 2
    Slope of both lines are 4, -4 respectively
    Since slope are not equal then both are not parallel.
    Product of both slope is 4 × -4 = -16
    So, both are not perpendicular also.
    So,
    Both are nor parallel neither perpendicular.

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 4 x plus 1 space straight & space y equals negative 4 x minus 2

    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 = 4x + 1
    y = -4x - 2
    Slope of both lines are 4, -4 respectively
    Since slope are not equal then both are not parallel.
    Product of both slope is 4 × -4 = -16
    So, both are not perpendicular also.
    So,
    Both are nor parallel neither perpendicular.

    General
    Maths-

    Write recursive formula and find the first term. a subscript n equals 10 plus 8 n

    • We have given a explicit function a subscript n equals 10 plus 8 n.
    • We have to find the recursive formula and first term.
    Step 1 of 2:
    We have given explicit formula a subscript n equals 10 plus 8 n.
    First term 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 a subscript n equals 10 plus 8 n end cell row cell a subscript 1 equals 10 plus 8 left parenthesis 1 right parenthesis end cell row cell a subscript 1 equals 18 end cell end table
    Step 2 of 2:
    Now for recursive formula we will calculate .
    So,

    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 10 plus 8 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 10 plus 8 n minus 8 end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 8 end cell end table
    .

    Write recursive formula and find the first term. a subscript n equals 10 plus 8 n

    Maths-General
    • We have given a explicit function a subscript n equals 10 plus 8 n.
    • We have to find the recursive formula and first term.
    Step 1 of 2:
    We have given explicit formula a subscript n equals 10 plus 8 n.
    First term 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 a subscript n equals 10 plus 8 n end cell row cell a subscript 1 equals 10 plus 8 left parenthesis 1 right parenthesis end cell row cell a subscript 1 equals 18 end cell end table
    Step 2 of 2:
    Now for recursive formula we will calculate .
    So,

    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 10 plus 8 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 10 plus 8 n minus 8 end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 8 end cell end table
    .

    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    x minus 3 y equals 6 space straight & space x minus 3 y equals 9

    • 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

    x - 3y = 6
    x - 3y = 9
    Slope of both lines are 1 third comma 1 third respectively
    Since slope are  equal then both are parallel.

    Are graphs of the equations parallel, perpendicular or neither?
    x minus 3 y equals 6 space straight & space x minus 3 y equals 9

    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

    x - 3y = 6
    x - 3y = 9
    Slope of both lines are 1 third comma 1 third respectively
    Since slope are  equal then both are parallel.

    parallel
    General
    Maths-

    What is the graph of f left parenthesis x right parenthesis equals fraction numerator 4 x squared minus 9 over denominator x squared plus 2 x minus 15 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 + 2x - 15= 0
    x2 + 5x -3x - 15= 0
    x(x + 5) - 3 (x + 5) = 0
    (x – 3) (x + 5) = 0
    x – 3 = 0   or    x + 5 = 0
    x = 3   or   x = -5
    The vertical asymptote of the rational function is x = 3 and x = -5  .
    This function has the x - intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

    What is the graph of f left parenthesis x right parenthesis equals fraction numerator 4 x squared minus 9 over denominator x squared plus 2 x minus 15 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 + 2x - 15= 0
    x2 + 5x -3x - 15= 0
    x(x + 5) - 3 (x + 5) = 0
    (x – 3) (x + 5) = 0
    x – 3 = 0   or    x + 5 = 0
    x = 3   or   x = -5
    The vertical asymptote of the rational function is x = 3 and x = -5  .
    This function has the x - intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

    General
    Maths-

    Find the equation for a path that passes through the point (-4, 9) and is parallel to y equals negative 3 over 4 x plus 1.

    • We have been given an equation that represents y-axis.
    • We have to find an equation for a path that passes through the point (-4,9) and is perpendicular to y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Step 1 of 1:
    We have given a line passes through a point (-4, 9) and parallel to a line y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Since two parallel lines have same slope.
    So, Slope of the line will be fraction numerator negative 3 over denominator 4 end fraction
    Therefore the equation of the line will be

     y minus 9 equals fraction numerator negative 3 over denominator 4 end fraction left parenthesis x plus 4 right parenthesis

    y equals fraction numerator negative 3 over denominator 4 end fraction x plus 6

    Find the equation for a path that passes through the point (-4, 9) and is parallel to y equals negative 3 over 4 x plus 1.

    Maths-General
    • We have been given an equation that represents y-axis.
    • We have to find an equation for a path that passes through the point (-4,9) and is perpendicular to y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Step 1 of 1:
    We have given a line passes through a point (-4, 9) and parallel to a line y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Since two parallel lines have same slope.
    So, Slope of the line will be fraction numerator negative 3 over denominator 4 end fraction
    Therefore the equation of the line will be

     y minus 9 equals fraction numerator negative 3 over denominator 4 end fraction left parenthesis x plus 4 right parenthesis

    y equals fraction numerator negative 3 over denominator 4 end fraction x plus 6

    General
    Maths-

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript minus 7 semicolon a subscript 1 equals negative 3

    • We have given a subscript n equals a subscript n minus 1 end subscript minus 7 comma a subscript 1 equals negative 3
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript minus 7
    So, d = -7
    Also, We have a1 = -3
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals negative 3 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 7 right parenthesis end cell row cell a subscript n equals 4 minus 7 n. end cell end table
    .

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript minus 7 semicolon a subscript 1 equals negative 3

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript minus 7 comma a subscript 1 equals negative 3
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript minus 7
    So, d = -7
    Also, We have a1 = -3
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals negative 3 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 7 right parenthesis end cell row cell a subscript n equals 4 minus 7 n. end cell end table
    .

    parallel
    General
    Maths-

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript plus 1 semicolon a subscript 1 equals 12

    • We have given a subscript n equals a subscript n minus 1 end subscript plus 1 comma a subscript 1 equals 12
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript plus 1
    So, d = 1
    Also, We have a1 = 12
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 12 plus left parenthesis n minus 1 right parenthesis left parenthesis 1 right parenthesis end cell row cell a subscript n equals 11 plus n end cell end table

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript plus 1 semicolon a subscript 1 equals 12

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript plus 1 comma a subscript 1 equals 12
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript plus 1
    So, d = 1
    Also, We have a1 = 12
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 12 plus left parenthesis n minus 1 right parenthesis left parenthesis 1 right parenthesis end cell row cell a subscript n equals 11 plus n end cell end table

    General
    Maths-

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56

    • We have given a subscript n equals a subscript n minus 1 end subscript minus 21 comma a subscript 1 equals 56
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript minus 21
    So, d = -21
    Also, We have a1 = 56
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 56 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 21 right parenthesis end cell row cell a subscript n equals 77 minus 21 n end cell end table

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript minus 21 comma a subscript 1 equals 56
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript minus 21
    So, d = -21
    Also, We have a1 = 56
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 56 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 21 right parenthesis end cell row cell a subscript n equals 77 minus 21 n end cell end table

    General
    Maths-

    Graph each function g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 1 end fraction

    Hint :-
    Solution:-
    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 .
    x - 1= 0
    x = 1
    The vertical asymptote of the rational function is x= 1
    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 = 1 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 3 over 1=3

    Graph each function g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 1 end fraction

    Maths-General
    Hint :-
    Solution:-
    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 .
    x - 1= 0
    x = 1
    The vertical asymptote of the rational function is x= 1
    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 = 1 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 3 over 1=3
    parallel
    General
    Maths-

    Find the equation for a path that passes through the point (6, 6) and is perpendicular to y equals negative 3 over 4 x plus 1.

    • We have been given an equation that represents y-axis.
    • We have to find an equation for a path that passes through the point (6, 6) and is perpendicular to y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Step 1 of 1:
    We have given a line passes through a point (6, 6) and perpendicular to a line y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times fraction numerator negative 3 over denominator 4 end fraction equals negative 1

    m equals 4 over 3
    Therefore the equation of the line will be

    y minus 6 equals 4 over 3 left parenthesis x minus 6 right parenthesis

    y equals 4 over 3 x minus 2

    Find the equation for a path that passes through the point (6, 6) and is perpendicular to y equals negative 3 over 4 x plus 1.

    Maths-General
    • We have been given an equation that represents y-axis.
    • We have to find an equation for a path that passes through the point (6, 6) and is perpendicular to y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Step 1 of 1:
    We have given a line passes through a point (6, 6) and perpendicular to a line y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times fraction numerator negative 3 over denominator 4 end fraction equals negative 1

    m equals 4 over 3
    Therefore the equation of the line will be

    y minus 6 equals 4 over 3 left parenthesis x minus 6 right parenthesis

    y equals 4 over 3 x minus 2

    General
    Maths-

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1

    • We have given a subscript n equals a subscript n minus 1 end subscript minus 2 comma a subscript 1 equals negative 1
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript minus 2
    So, d = -2
    Also, We have a subscript 1 equals negative 1
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals negative 1 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 2 right parenthesis end cell row cell a subscript n equals 1 minus 2 n end cell end table

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript minus 2 comma a subscript 1 equals negative 1
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript minus 2
    So, d = -2
    Also, We have a subscript 1 equals negative 1
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals negative 1 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 2 right parenthesis end cell row cell a subscript n equals 1 minus 2 n end cell end table

    General
    Maths-

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9

    • We have given a subscript n equals a subscript n minus 1 end subscript plus 6 comma a subscript 1 equals 9
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript plus 6
    So, d = 6
    Also, We have a1 = 9
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 9 plus left parenthesis n minus 1 right parenthesis 6 end cell row cell a subscript n equals 6 n plus 3 end cell end table

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript plus 6 comma a subscript 1 equals 9
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript plus 6
    So, d = 6
    Also, We have a1 = 9
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 9 plus left parenthesis n minus 1 right parenthesis 6 end cell row cell a subscript n equals 6 n plus 3 end cell end table

    parallel
    General
    Maths-

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8

    • We have given a subscript n equals a subscript n minus 1 end subscript plus 15 comma a subscript 1 equals 8
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript plus 15
    So, d = 15
    Also, We have a1 = 8
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 8 plus left parenthesis n minus 1 right parenthesis 15 end cell row cell a subscript n equals 15 n minus 7 end cell end table

    Write explicit formula. a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript plus 15 comma a subscript 1 equals 8
    • We have to find the explicit formula of the given sequence.
    Step 1 of 1:
    We know that the recursive formula of an AP is a subscript n equals a subscript n minus 1 end subscript plus d, where d is common difference.
    Here we have a subscript n equals a subscript n minus 1 end subscript plus 15
    So, d = 15
    Also, We have a1 = 8
    So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 8 plus left parenthesis n minus 1 right parenthesis 15 end cell row cell a subscript n equals 15 n minus 7 end cell end table

    General
    Maths-

    Graph each function f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 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 .
    x + 8= 0
    x = -8
    The vertical asymptote of the rational function is x=-8
    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= -8 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 4 over 1= 4

    Graph each function f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 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 .
    x + 8= 0
    x = -8
    The vertical asymptote of the rational function is x=-8
    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= -8 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 4 over 1= 4
    General
    Maths-

    What is the graph of the functionf left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 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 .
    3x - 4= 0
    3x = 4
    x = 4 over 3
    The vertical asymptote of the rational function is x=4 over 3
    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= 4 over 3. and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 3
     

    What is the graph of the functionf left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 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 .
    3x - 4= 0
    3x = 4
    x = 4 over 3
    The vertical asymptote of the rational function is x=4 over 3
    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= 4 over 3. and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 3
     
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.