Mark the correct alternative in each of the following:

If the sum of first two terms of an infinite GP is 1 and every term is twice the sum of all the successive terms, then its first term is


Let the first term be a and the common ratio be r.


Sum of infinite terms is given by



The general term of any GP is given by arn.


The infinite sum of all successive terms is


(arn)r + (arn)r2 + (arn)r3 + ...


=


Therefore



1-r = 2r


r = 1/3.


Also given that


a+ar = a(1+r) = 1.


a = 1/(1+r) = 3/4.

1