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How many terms of G.P. 2,4,8,16, …………… are required to give sum 254?(a) 4(b) 5(c) 6(d) 7This question was posed to me in an international level competition.This key question is from Geometric Progression(G.P.) in chapter Sequences and Series of Mathematics – Class 11

Answer» RIGHT answer is (d) 7

To EXPLAIN I would say: a=2 and r = 4/2 = 2.

We KNOW, SN = a(r^n-1)/(r-1)

2(2^n-1) / (2-1) = 254

=>2^n-1 = 127 => 2^n = 128 = 2^7

=> n=7.


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