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-

Question Number 43603 by peter frank last updated on 12/Sep/18

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

Answered by $@ty@m last updated on 12/Sep/18

a + a r = 1

\Rightarrow a = \frac{1}{1 + r} . . (1)

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

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

\Rightarrow 1 - r = 2 r

\Rightarrow r = \frac{1}{3} . . (2)

∴ a = \frac{1}{1 + \frac{1}{3}}, f r o m (1)

\Rightarrow a = \frac{3}{4} A n s .

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