(Q12).Which term of the G.P.

(iii)
1
3
 ,
1
9
 ,
1
27
 , ......... is
1
2187
 ?

Given G.P.:
1
3
 ,
1
9
 ,
1
27
 , ......... is
1
2187
a =
1
 , r =
a2
a1
 =
1
1
 =
1
 ×
=
Let
1
2187
 be the nth term of the G.P., then
an = a . rn-1 =
1
2187
⇒
1
 × (
1
 )n-1 =
1
2187
⇒ (
1
 )n-1+1 = (
1
 )7
⇒ (
1
 )n = (
1
 )7

⇒ n =

∴ 2187 = × × × × × ×

= 7

∴
1
2187
 = (
1
 )7

[∵ bases are equal, exponents are also equal]

∴ th term of G.P is
1
2187