Question

In a GP{a_n}, if a₁ = 3, a_n = 96 and S_n = 189. Find common ratio and n.

Answer 1

Given; a₁ = 3, a_n = 96 ⇒ ar^n-1 = 96

⇒ 3 × r^n-1 = 96 ⇒ r^n-1 = 32 = 2⁵

⇒ r^n-1 = 2⁵

Then, r = 2; n = 6.