Math 12

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sum of 2nd and 5th terms of a geometric sequence is 13. the sum of the 3rd and 6th is -39.

determine:
a) the ratio "r" of the sequence
b) the first term "a" of the sequence

  • Math 12 -

    The sequence is or the form
    a(1 + r + r^2 + ...)
    The first term is a1 = a
    The second term is a2 =a*r
    The nth term is an = a*r^*(n-1)

    Here is what you know:
    a*r + a*r^4 = 13
    a*r^2 + a*r^5 = -39
    These two equations require that
    -39 = r*13. Therefore
    r = -3

    Now that you know r, solve the first equation for a:
    a*(-3 + 81) = 13
    78 a = 13
    a = 1/6

    The sequence is:
    1/6, -1/2, 3/2, -9/2, 27/2, -81/2 ...

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