Given G.P.: 2, 8, 32,….. is 512
a = 2, r = \(\frac{a_2}{a_1}\) = \(\frac{8}{2}\) = 4
Let the nth term of G.P. be 512
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 29
∴ 2n – 1 = 9 [∵ bases are equal, exponents are also equal]
∴ 2n = 9 + 1 = 10
n = 10/2 = 5
∴ 512 is the 5th term of the given G.P.