The sum of first two terms of a G.P. is 1 and every term is twice the previous term.

Question:

The sum of first two terms of a G.P. is 1 and every term is twice the previous term. The first term of the G.P. is ____________.

Solution:

Let a, ar, ar2, ....... arn–1 defines a G.P

According to given condition,

ar = 2a

i.e r = 2 and a + ar = 1

a(1 + r) = 1

a(1 + 2) = 1

i. e $a=\frac{1}{3}$

i.e first term of g.p is $\frac{1}{3}$

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