Question

The sum of first two terms of an infinite gp is 1 and every term is twice the sum of successive terms .. find its first term .

Answer 1

☆☆ranshsangwan☆☆

Suppose the 1st term is a and the common ratio is r. The infinite sum of the series is a/(1-r). 

The general term is ar^n. The (infinite) sum of all successive terms is 
(ar^n)r + (ar^n)r^2 + (ar^n)r^3 + ... 
= (ar^n)r/(1-r). 
Therefore 
ar^n = 2(ar^n)r/(1-r) 
1-r = 2r 
r = 1/3. 

We are also given that 
a+ar = a(1+r) = 1. 
So 
a = 1/(1+r) = 3/4. 

ANSWER : a = 3/4.