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
• B. n
• C. m
• D. m+n

Answer 1

The correct option is A

0

As given $\frac{n}{2}${2a + (n-1)d} = $\frac{m}{2}${a + (m-1)d}

⇒2a(m-n) + d( $m^2$ - m - $n^2$ + n) = 0

⇒(m - n){2a + d(m + n - 1)} = 0

⇒2a + (m + n - 1)d = 0, ( ∵ m ≠ n)

∴ $S_{m+n}$ = $\frac{m+n}{2}${2a + (m + n - 1)d} = $\frac{m+n}{2}${0} = 0