The-sum-of-first-two-terms-of-an-infinite-GP-is-1-and-every-term-is-twice-the-sum-of-the-successive-terms-Its-first-term-is-

Question Number 46921 by 786786AM last updated on 02/Nov/18

The sum of first two terms of an infinite

GP is 1 and every term is twice the sum

of the successive terms . Its first term is

Answered by peter frank last updated on 02/Nov/18

a + ar = 1 \dots . . (1)

a = 2 (ar + {ar}^{2} + {ar}^{3} + \dots) \dots (2)

from 1

a = \frac{1}{1 + r}

from 2

a = \frac{2 ar}{1 - r}

1 - r = 2 r

r = \frac{1}{3}

substitute r in 1

a = \frac{3}{4}