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 find its first term

Answers

Question :

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 find its first term ?
Submitted on 10/7/2024 | Answered by Vandana Rana

Answer :

Let terms of infinite G.P. are a,ar ,ar²....

.......
a +ar =1.........

(1)
a =2(ar +ar²+ar³+.......)(given)
a =2ar(1+r+r²+.........)
1 =2r[1/(1-r)]
1-r=2r
3r= 1
r =1/3
put value of in (1)
a(1 +1/3) =1
a=3/4