(Q10).Which term of the G.P.

(i) 2, 8, 32,….. is 512?

Given G.P.: 2, 8, 32,….. is 512

a = , r =
a2
a1
 =
=

Let the nth term of G.P. be 512

an = a.rn-1

= × ()n-1

9 = × (2)n-1

9 = 1 × 2(n-1)

9 = 2n-2+1

9 = 2n-1

512 = × × × × × × × ×

= 9

∴ n – 1 =

[∵ bases are equal, exponents are also equal]

∴ n = + 1 =

n =
=

∴ 512 is the th term of the given G.P.