Maths-
General
Easy

Question

Write recursive formula. -5,-8.5,-12,-15.5,-19,....

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: a_n=a_(n-1)-3.5.


    Explanation:
    • We have given a sequence -5,-8.5,-12,-15.5,-19,....
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given a sequence -5,-8.5,-12,-15.5,-19,....
    The given sequence is an AP
    And we know the recursive formula of 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 -3.5.
    So, The recursive formula is

    a subscript n equals a subscript n minus 1 end subscript minus 3.5

    Related Questions to study

    General
    Maths-

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis negative 2 comma 5 right parenthesis semicolon space x equals 3

    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (-2, 5) and perpendicular to a line x = 3
    Since product of two perpendicular lines is equal to -1.
    So,

    m × ∞ = -1
    m = 0
    Therefore the equation of the line will be

    y - 5 = 0 (x + 2)
    y = 5.

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis negative 2 comma 5 right parenthesis semicolon space x equals 3

    Maths-General
    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (-2, 5) and perpendicular to a line x = 3
    Since product of two perpendicular lines is equal to -1.
    So,

    m × ∞ = -1
    m = 0
    Therefore the equation of the line will be

    y - 5 = 0 (x + 2)
    y = 5.

    General
    Maths-

    Find the vertical and horizontal asymptotes of rational function, then graph the function.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 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 .
    2x + 1 = 0
    x = fraction numerator negative 1 over denominator 2 end fraction
    The vertical asymptote of the rational function is x = fraction numerator negative 1 over denominator 2 end fraction
    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= fraction numerator negative 1 over denominator 2 end fraction and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 half=0.5

    Find the vertical and horizontal asymptotes of rational function, then graph the function.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 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 .
    2x + 1 = 0
    x = fraction numerator negative 1 over denominator 2 end fraction
    The vertical asymptote of the rational function is x = fraction numerator negative 1 over denominator 2 end fraction
    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= fraction numerator negative 1 over denominator 2 end fraction and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 half=0.5
    General
    Maths-

    Write recursive formula. 2,6,10,14,18,....

    • We have given a sequence 2,6,10,14,18,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given a sequence 2,6,10,14,18,...
    The given sequence is an AP
    And we know the recursive formula of 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 4

    Write recursive formula. 2,6,10,14,18,....

    Maths-General
    • We have given a sequence 2,6,10,14,18,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given a sequence 2,6,10,14,18,...
    The given sequence is an AP
    And we know the recursive formula of 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 4

    parallel
    General
    Maths-

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis 0 comma 3 right parenthesis semicolon space 3 x minus 4 y equals negative 8

    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (0, 3) and perpendicular to a line 3x - 4y = -8
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times 3 over 4 equals negative 1

    m equals fraction numerator negative 4 over denominator 3 end fraction
    Therefore the equation of the line will be

    y minus 3 equals fraction numerator negative 4 over denominator 3 end fraction left parenthesis x minus 0 right parenthesis

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

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis 0 comma 3 right parenthesis semicolon space 3 x minus 4 y equals negative 8

    Maths-General
    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (0, 3) and perpendicular to a line 3x - 4y = -8
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times 3 over 4 equals negative 1

    m equals fraction numerator negative 4 over denominator 3 end fraction
    Therefore the equation of the line will be

    y minus 3 equals fraction numerator negative 4 over denominator 3 end fraction left parenthesis x minus 0 right parenthesis

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

    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. -6,5,16,27,38,....

    • We have given a sequence -6,5,16,27,38,....
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence -6,5,16,27,38,....
    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 5 minus left parenthesis negative 6 right parenthesis end cell row cell not stretchy rightwards double arrow 11 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 16 minus 5 end cell row cell not stretchy rightwards double arrow 11 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 27 minus 16 end cell row cell not stretchy rightwards double arrow 11 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. -6,5,16,27,38,....

    Maths-General
    • We have given a sequence -6,5,16,27,38,....
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence -6,5,16,27,38,....
    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 5 minus left parenthesis negative 6 right parenthesis end cell row cell not stretchy rightwards double arrow 11 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 16 minus 5 end cell row cell not stretchy rightwards double arrow 11 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 27 minus 16 end cell row cell not stretchy rightwards double arrow 11 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. 48,45,42,39,....

    • We have given a sequence 48,45,42,39,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 48,45,42,39,...
    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 42 minus 45 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 42 minus 45 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 39 minus 42 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. 48,45,42,39,....

    Maths-General
    • We have given a sequence 48,45,42,39,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 48,45,42,39,...
    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 42 minus 45 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 42 minus 45 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 39 minus 42 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.

    parallel
    General
    Maths-

    Find the vertical and horizontal asymptotes of rational function, then graph the function.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 2 over denominator x minus 3 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 - 3 = 0
    x = 3
    The vertical asymptote of the rational function is x = 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 = 3 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 over 1=1

    Find the vertical and horizontal asymptotes of rational function, then graph the function.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 2 over denominator x minus 3 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 - 3 = 0
    x = 3
    The vertical asymptote of the rational function is x = 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 = 3 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 over 1=1
    General
    Maths-

    Which sequence is an arithmetic sequence?

    • We have given a sequence 1,3,5,7,11,....
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    Option(A):
    We have given a sequence 1,3,5,7,11,....
    The common difference here is not constant, as 3 - 1 ≠ 11 - 7
    So, This is not an AP.
    Option(B):
    We have given a sequence 4,6,9,13,18,....
    The common difference here is not constant, as 6 - 4 ≠ 9 - 6
    So, This is not an AP.
    Step 2 of 2:
    Option(c):
    We have given a sequence 8,15,22,29,36,....
    The common difference here is constant.
    So, This is an AP.
    Option(D):
    We have given a sequence 3,6,12,24,48,....
    The common difference here is not constant, as 6 - 3 ≠ 12 - 6
    So, This is not an AP.

    Which sequence is an arithmetic sequence?

    Maths-General
    • We have given a sequence 1,3,5,7,11,....
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    Option(A):
    We have given a sequence 1,3,5,7,11,....
    The common difference here is not constant, as 3 - 1 ≠ 11 - 7
    So, This is not an AP.
    Option(B):
    We have given a sequence 4,6,9,13,18,....
    The common difference here is not constant, as 6 - 4 ≠ 9 - 6
    So, This is not an AP.
    Step 2 of 2:
    Option(c):
    We have given a sequence 8,15,22,29,36,....
    The common difference here is constant.
    So, This is an AP.
    Option(D):
    We have given a sequence 3,6,12,24,48,....
    The common difference here is not constant, as 6 - 3 ≠ 12 - 6
    So, This is not an AP.
    General
    Maths-

    Write an equation of a line that passes through the given line and is perpendicular to the given line.

    left parenthesis negative 6 comma negative 3 right parenthesis semicolon y equals negative 2 over 5 x

    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (-6, -3) and perpendicular to a line y equals fraction numerator negative 2 over denominator 5 end fraction x
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times fraction numerator negative 2 over denominator 5 end fraction equals negative 1

    m equals 5 over 2
    Therefore the equation of the line will be

    y plus 3 equals 5 over 2 left parenthesis x plus 6 right parenthesis

    y equals 5 over 2 x plus 12.

    Write an equation of a line that passes through the given line and is perpendicular to the given line.

    left parenthesis negative 6 comma negative 3 right parenthesis semicolon y equals negative 2 over 5 x

    Maths-General
    • We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (-6, -3) and perpendicular to a line y equals fraction numerator negative 2 over denominator 5 end fraction x
    Since product of two perpendicular lines is equal to -1.
    So,

    m cross times fraction numerator negative 2 over denominator 5 end fraction equals negative 1

    m equals 5 over 2
    Therefore the equation of the line will be

    y plus 3 equals 5 over 2 left parenthesis x plus 6 right parenthesis

    y equals 5 over 2 x plus 12.

    parallel
    General
    Maths-

    When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.


    For example, function f ( x ) = fraction numerator negative 1 over denominator left parenthesis x squared plus 4 right parenthesis end fraction​ has no vertical asymptote.

    When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.

    Maths-General
    • If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
    • If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
    • If the degree of the numerator is greater than the denominator, then there is no vertical asymptote.

    For example, function f ( x ) = fraction numerator negative 1 over denominator left parenthesis x squared plus 4 right parenthesis end fraction​ has no vertical asymptote.
    General
    Maths-

    Write an equation of a line that passes through the given line and is parallel to the given line.
    left parenthesis 6 comma 4 right parenthesis semicolon space 2 x plus 3 y equals 18

    • We have to write an equation of a line that passes through the given line and is parallel to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (6, 4) and parallel to a line 2x + 3y = 18
    Since two parallel lines have same slope.
    So, Slope of the line will be fraction numerator negative 2 over denominator 3 end fraction
    Therefore the equation of the line will be

    y minus 4 equals fraction numerator negative 2 over denominator 3 end fraction left parenthesis x minus 6 right parenthesis

    y equals fraction numerator negative 2 over denominator 3 end fraction x plus 8

    Write an equation of a line that passes through the given line and is parallel to the given line.
    left parenthesis 6 comma 4 right parenthesis semicolon space 2 x plus 3 y equals 18

    Maths-General
    • We have to write an equation of a line that passes through the given line and is parallel to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (6, 4) and parallel to a line 2x + 3y = 18
    Since two parallel lines have same slope.
    So, Slope of the line will be fraction numerator negative 2 over denominator 3 end fraction
    Therefore the equation of the line will be

    y minus 4 equals fraction numerator negative 2 over denominator 3 end fraction left parenthesis x minus 6 right parenthesis

    y equals fraction numerator negative 2 over denominator 3 end fraction x plus 8

    General
    Maths-

    Asthon said the graph of f left parenthesis x right parenthesis equals fraction numerator x plus 2 over denominator 2 x squared plus 4 x minus 6 end fraction has a horizontal asymptote at y equals 0.5 . Describe and correct Asthon's error.

    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 .
    2x2 + 4x - 6= 0
    x2 + 2x - 3= 0
    x2 + 3x – x – 3 = 0
    x(x + 3) – (x - 3) = 0
    (x - 1) (x + 3) = 0
    x = -3  or  x = 2 over 2 = 1
    The vertical asymptote of the rational function is x= 2.24 and x= -2.24  .
    We will find more points on the function and graph the function.


    the degree of the numerator is less than the denominator, then the horizontal asymptote is located at y = 0 (which is the x-axis).

    Asthon said the graph of f left parenthesis x right parenthesis equals fraction numerator x plus 2 over denominator 2 x squared plus 4 x minus 6 end fraction has a horizontal asymptote at y equals 0.5 . Describe and correct Asthon's error.

    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 .
    2x2 + 4x - 6= 0
    x2 + 2x - 3= 0
    x2 + 3x – x – 3 = 0
    x(x + 3) – (x - 3) = 0
    (x - 1) (x + 3) = 0
    x = -3  or  x = 2 over 2 = 1
    The vertical asymptote of the rational function is x= 2.24 and x= -2.24  .
    We will find more points on the function and graph the function.


    the degree of the numerator is less than the denominator, then the horizontal asymptote is located at y = 0 (which is the x-axis).
    parallel
    General
    Maths-

    Write an equation of a line that passes through the given line and is parallel to the given line.
    left parenthesis negative 3 comma 2 right parenthesis semicolon space y equals negative 4

    • We have to write an equation of a line that passes through the given line and is parallel to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (-3, 2) and parallel to a line y = -4
    Since two parallel lines have same slope.
    So, Slope of the line will be 0
    Therefore the equation of the line will be

    y - 2 = 0 (x + 3)
    y = 2

    Write an equation of a line that passes through the given line and is parallel to the given line.
    left parenthesis negative 3 comma 2 right parenthesis semicolon space y equals negative 4

    Maths-General
    • We have to write an equation of a line that passes through the given line and is parallel to the given line.
    Step 1 of 1:
    We have to find a line passes through a point (-3, 2) and parallel to a line y = -4
    Since two parallel lines have same slope.
    So, Slope of the line will be 0
    Therefore the equation of the line will be

    y - 2 = 0 (x + 3)
    y = 2

    General
    Maths-

    Write recursive formula and find the first term. a subscript n equals 7 plus 1 fourth n

    • We have given a explicit function a subscript n equals 7 plus 1 fourth n.
    • We have to find the recursive formula and first term.
    Step 1 of 2:
    We have given explicit formula a subscript n equals 7 plus 1 fourth 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 7 plus 1 fourth n end cell row cell a subscript n equals 7 plus 1 fourth left parenthesis 1 right parenthesis end cell row cell a subscript n equals 29 over 4 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 7 plus 1 fourth left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 7 plus 1 fourth n minus 1 fourth end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 1 fourth end cell row cell a subscript n equals a subscript n minus 1 end subscript plus 1 fourth end cell end table

    Write recursive formula and find the first term. a subscript n equals 7 plus 1 fourth n

    Maths-General
    • We have given a explicit function a subscript n equals 7 plus 1 fourth n.
    • We have to find the recursive formula and first term.
    Step 1 of 2:
    We have given explicit formula a subscript n equals 7 plus 1 fourth 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 7 plus 1 fourth n end cell row cell a subscript n equals 7 plus 1 fourth left parenthesis 1 right parenthesis end cell row cell a subscript n equals 29 over 4 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 7 plus 1 fourth left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 7 plus 1 fourth n minus 1 fourth end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 1 fourth end cell row cell a subscript n equals a subscript n minus 1 end subscript plus 1 fourth end cell end table

    General
    Maths-

    How can you graph a rational function ?

    A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =fraction numerator straight p left parenthesis straight x right parenthesis over denominator straight q left parenthesis straight x right parenthesis end fraction, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
    Rational functions are of the form y=f(x)y=fx , where f(x)fx is a 
    rational expression .
    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.

    How can you graph a rational function ?

    Maths-General
    A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =fraction numerator straight p left parenthesis straight x right parenthesis over denominator straight q left parenthesis straight x right parenthesis end fraction, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
    Rational functions are of the form y=f(x)y=fx , where f(x)fx is a rational expression .
    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.
    parallel

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