Latest Elitmus Aptitude Question SOLUTION: in an infinite geomatric progression,each term is equal to 2 times the sum of the terms that follow.if the first term of the series is 8,find the sum of the series. a)12 b)32/3

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in an infinite geomatric progression,each term is equal to 2 times the sum of the terms that follow.if the first term of the series is 8,find the sum of the series.
a)12 b)32/3
c)34/3 d)No any

Asked In Elitmus Javlak Mansuri (6 years ago)

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Nikita  (6 years ago)

ans is 12.
let 8=a/r,next term is a,next term ar and so on
as per ques
8=2(a+ar+ar2+ar3+...........infinity)
8=2*a/1-r
a/r=2*a/1-r
r=1/3
sum of infinite term of gp is
1st term/1-r= 12

Is this solution Helpfull? Yes (9) | No (2)  

vijay pandey  (6 years ago)

Let the terms are ... a, ar, ar2, ar3,............infinity.
as per ques,
a=2(ar+ar2+ar3+...........infinity),
=>a=2(a+ar+ar2+ar3+...........infinity - a),
=>a=2(a/1-r) - 2a..............................bcz S(infinity)=(a/1-r),
=>a=2a(r/1-r),
=>1=2(r/1-r),
=>r=1/3
Therefore, sum of infinite term of GP is = a/1-r
After putting value of a=8 and r=1/3,
we get sum of infinite term of GP is = 12. Ans.

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Abhishek Kumar Soni  (6 years ago)

For the geometric series, a+ar+ar2+... with |r|

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