Question

How many terms of a geometric progression 2, 4, 8, 16, … would add to 126?

Answer 1

Here. GP. is 2; 4, 8, 16,…

∴ a = 2, r = 4 / 2 =2, S_n = 126. n =?

Now, S_n = r-1 (,r > 1)

∴ 126 = \(\frac{2[2^n−1]}{2−1}\)

∴ 126 / 2 = 2ⁿ – 1

∴ 63 + 1 = 2ⁿ

∴ (2)⁶ = 2ⁿ

∴ n = 6