Find the 12^th term of a G.P. whose 8^th term is 192 and the common ratio is 2.

Given: 8^th of the G.P. is 192 and common ratio is 2.

That is,

a₈ = 192 and r = 2.

We know that in G.P a_n = ar^n-1

Here, n: number of terms

a: First term = 5/2

r: common ratio

∴ a₈ = a(2)^8-1 (∵ r = 2 and n = 8)

⇒ 192 = a(2)⁷

⇒ a × 128 = 192

Now,

∴ a₁₂ = 3072