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In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
Let the series be 
a +ar + ar² + ar³ +ar⁴+.......
According to question
a = 3(ar +ar² +ar³+.....)
a = 3*ar/(1-r)
1-r = 3r
r = ¼
Also given that
a +ar = 15 
Hence
a(1+1/4) = 15
a *(5/4) = 15
a = 12
 
Hence
Sum of series to infinity = a/(1-r) = 12/(1-1/4)
= 48/3 = 16
 
Regards
Arun (askIITians forum expert)

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