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Question

If 3+5+7+.....to n terms5+8+11+...to 10 terms=7, then n is equal to

A

35
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B

36
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C

37
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D

38
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Solution

The correct option is A
35
3+5+7+.....to n terms5+8+11+...to 10 terms=7Sn=n2(2a+(n1)d)n2[2×3+(n1)2]102[2×5+(101)×3]=7n[6+2n2]10[10+27]=7n×2(n+2)10×37=7n2+2n=7×5×37n2+2n=1295n2+2n1295=0n2+37n35n1295=0n(n+37)35(n+37)=0(n+37)(n35)=0n+37=0 n35=0 n=37 or n=35
Hence, a is the correct option.

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