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Question

The sum of an infinite geometric series is 512 and sum of first n terms is 510 (n>1) . If the inverse of its common ratio is an integer then which of this following can not be the second term of the series?

A
30
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B
96
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C
256
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D
128
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Solution

The correct option is C 256
Let a be the 1st term of the series and r be thier common ratio.
S=a1r=512
and
Sn=a(1rn)1r=510
SSn=256255=11rnrn=1256
Since, 1r is given as an integer and n is always an integer therefore,
(1r)n=256
1r can be 2,4,16 for n=8,4,2
a=256,384,480a2=128,96,30

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