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Question

If S2n=3Sn and S5n=kS3n, where Sn is the sum of n terms of an A.P., then the value of k is

A
2
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B
2.5
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C
3
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D
3.5
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Solution

The correct option is B 2.5
Given: S2nSn=3
2n2[2a+(2n1)d]n2[2a+(n1)d]=32a=(n+1)d ...(1)

S5nS3n=5n2[2a+(5n1)d]3n2[2a+(3n1)d]k=5[(n+1)d+(5n1)d]3[(n+1)d+(3n1)d]k=5×6nd3×4ndk=2.5

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