Question

If the sum of first two terms of an infinite G.P is 1 and every term is twice the sum of all the successive terms then its first term is​

Answer 1

Step-by-step explanation:

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.

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