Question

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

Answer 1

Common ratio, r = 2

Let a be the first term of the G.P.

∴ a8 = ar 8–1 = ar7

⇒ ar7 = 192

a(2) 7 = 192

a(2) 7 = (2)6 (3)

⇒a = (2)6 × \(\frac{3}{(2)}7=\frac{3}{2}\)

∴ a12 = ar12 - 1 = \((\frac{3}{2})\)(2)11 = (3)(2)10 = 3072