math C2 sequences and series

The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and common ratio r.
a)Given that d is not equal to 0,find the value of r
b)Given that A=2,find the sum to infinity of the geometric progression

asked by Stephan
  1. 8th term of AS = a+7d
    4th term of AS = a+3d
    2nd term of AS = a+d

    then, if they form the first three terms of a GS
    (a+3d)/(a+7d) = (a+d)/(a+3d)
    (a+3d)^2 = (a+7d)(a+d)
    a^2 + 6ad + 9d^2 = a^2 + 8ad + 7d^2
    2d^2 - 2ad = 0
    d(d-a) = 0
    d = 0 or d = a
    but we are told that d ≠ 0 , so
    d = a

    r = (a+3d)/(a+7d)
    = 4a/(8a) = 1/2

    f) if a = 2
    sum(all terms) = a/(1-r)
    = 2/(1 - 1/2)
    = 4

    posted by Reiny

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