Question

The sum of n terms of the G.P. 3, 6, 12, … is 381. Find the value of n.

Answer 1

Given:

Sum of GP = 381

Where, a = 3, r = 6/3 = 2, n = ?

By using the formula,

Sum of GP for n terms = a(rⁿ – 1 )/(r – 1)

381 = 3 (2ⁿ – 1)/ (2 - 1)

381 = 3 (2ⁿ – 1)

381/3 = 2ⁿ – 1

127 = 2ⁿ – 1

127 + 1 = 2ⁿ

128 = 2ⁿ

2⁷ = 2ⁿ

n = 7

∴ value of n is 7