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Question

Let Sn denote the sum of the first ′n′ terms of an A.P. S2n=3Sn. Then, the ratio S3nSn is equal to :

A
4
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B
6
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C
8
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D
10
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Solution

The correct option is D 6
S2n=3Sn
2n2(2a+(2n1)d)=3n2(2a+(n1)d)
4a+4nd2d=6a+3nd3d
nd +d = 2a ....(i)
S3nSn=3n2(2a+(3n1)d)n2(2a+(n1)d)
= 3n2(nd+d+(3n1)d)n2(nd+d+(n1)d)
= 3n2(4nd)n2(2nd)
= 6

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