Question

if fifth term of g.p. is 2. find the product of first nine term of g.p.

Answer 1

a = first term

r = common ratio

$T_5 = ar^4 = 2 \\ \\ P_9 = a(ar)(ar^2)(ar^3)(ar^4)(ar^5)(ar^6)(ar^7)(ar^8) \\ \\ = a^9r^{36} \\ \\ = (ar^4)^9 = 2^9 = 512$

512 is the answer.

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