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.