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Question

If Sn denotes the sum of the first n terms of an A.P and S3nSn1S2nS2n1=31, then the value of n is

A
21
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B
15
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C
16
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D
19
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Solution

The correct option is B 15
S3n=3n2[2a+(3n1)d] where a first term d common differ

S2n=2n2(2a+(2n1)d)

Sn1=(n1)2[2a+(n11)d]

S2n1=(2n1)2[2a+(2n11)d]

S3nSn1S2nS2n1=3n2[2a+(3n1)d](n1)2[2a+(n2)d]2n2[2a+(2n1)d](2n1)2[2a+(2n2)d]=31

=a(2n+1)+d(4n21]a+d[2n1)=(2n+1)[a+(2n1)d]a+(2n1)d=31

(2n+1)=31

n=15.

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