The 2nd, 5th, and 14th term Of an AP are consecutive terms of a GP. Given that the sum of the three terms of the AP is 9, find the

Question

A, first term and the common difference of the AP.
B common ratio of the GP
C sum of the first three terms of the GP

Answer 1

(a+4d)/(a+d) = (a+13d)/(a+4d)
a+d + a+4d + a+13d = 9

AP: a=3/13, d=6/13
T2 = 9/13
T5 = 27/13
T14 = 81/13

Clearly the have a common ratio of 3

Answer 2

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