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Question

The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of following terms, then the 4th term of the series is ____.

A
1
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B
14
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C
116
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D
18
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Solution

The correct option is B 116
a+ar=5
each term =3(sum of following terms)
arn1=3(arn+arn+1+....)arn1=3rn(a+ar+ar2+....)arn1=3arn1r3r1r=13r=1rr=14a+a4=5=>a=4
Fourth term of G.P =ar3=443=116

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