Q11 of 176 Page 21

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.

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