Find the sum to n terms of the sequence :
(i) 
,….. to n terms
(ii) (x + y), 9x2 + xy + y2), (x3 + x2y + xy2 + y3), …. to n terms
This can also be written as
= 
= 
= 
Sum of a G.P. series is represented by the formula, 
, when r≠1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.
a = 
r = (ratio between the n term and n-1 term) 
n terms
∴ 
⇒
⇒
⇒
∴ 
(ii) If we divide and multiply the terms by (x-y)
= 
= 
= 
Sum of a G.P. series is represented by the formula, 
, when r≠1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.
Here,
a = x2, y2
r = (ratio between the n term and n-1 term) x, y
n terms
∴ 
⇒