Question

If in a geometric progression {a_n}, a₁ = 3, a_n = 96 and S_n = 189, then the value of n is ______.

Options

• 5

• 6

• 7

• 8

Answer 1

If in a geometric progression {a_n}, a₁ = 3, a_n = 96 and S_n = 189, then the value of n is 6.

Explanation:

a₁ = 3,

a₁r^n–1 = 96, `(a_1(1 - r^n))/(1 - r)` = 189

⇒ r^n–1 = 32 and `(1 - r^n)/(1 - r)` = 63 

⇒ `(1 - 32r)/(1 - r)` = 63

⇒ r = 2

∵ 2^n–1 = 2⁵

⇒ n = 6