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Question

If the sum of frist n terms of an A.P. be equal to the sum of its

first m terms, (m ≠ n), then the sum of its first (m+n) terms

will be


A

0

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B

n

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C

m

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D

m+n

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Solution

The correct option is A

0


As given n2{2a + (n-1)d} = m2{a + (m-1)d}

⇒2a(m-n) + d( m2 - m - n2 + n) = 0

⇒(m - n){2a + d(m + n - 1)} = 0

⇒2a + (m + n - 1)d = 0, ( ∵ m ≠ n)

Sm+n = m+n2{2a + (m + n - 1)d} = m+n2{0} = 0


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