Question

How many terms of G.P. 2,4,8,16, …………… are required to give sum 254?

(a) 4

(b) 5

(c) 6

(d) 7

This 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 1

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.