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Question

# An AP has the property that the sum of first ten terms is half the sum of next ten terms. If the second term is 13, then the common difference is

A
3
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B
2
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C
5
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D
4
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E
6
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Solution

## The correct option is B 2Let a and d be the first term and common difference, respectively.Given, T2=13⇒a+d=13 .... (i)According to the question, we have(a1+a2+....+a10)=12(a11+a12+...+a20)⇒2(a1+a2+....+a10)=a11+a12+...+a20⇒3(a1+a2+....+a10)=(a1+a2+...+a20)(add a1+a2+...+a10 on both sides)⇒3×102[2a+9d]=202[2a+19d]⇒6a+27d=4a+38d⇒2a=11d .... (ii)From Eqs. (i) and (ii), we get11d2+d=13⇒13d2=13⇒d=2.

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