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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 its first term is 


Solution

(d) 34

Let the terms of the G.P. be a,a2,a3,a4,a5.......,

And, let the common ratio be r

Now, a+a2=1

a+ar=1              ........  (i)

Also, a=2(a2+a3+a4+a5+.......)

a=2(ar+ar2+ar3+ar4+......)

a=2(ar1r)

1r=2r

3r=1

r=13.

Putting the value of r in (i) :

a+a3=1

4a3=1

4a=3

a=34

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