The 4^th and 7^th terms of a GP are and respectively. Find the sum of n terms of the GP.

4^th term = ar^4-1 = ar³ =

7^th term = ar^7-1= ar⁶ =

Dividing the 7^th term by the 4^th term,

⇒ ……(i)

∴

ar³ = [putting from eqn (i) ]

a =

∴ a = 1

Sum of a G.P. series is represented by the formula, , when |r|<1. ‘S_n’ represents the sum of the G.P. series upto n^th terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.

Here,

a = 1

n terms

∴

⇒

⇒

∴