If $m$ th term of an A.P. is $n$ and $n$ th term is $m$ , then the $(m + n)$ th term is

0

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m + n - 1

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m + n

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\frac{m n}{m + n}

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Solution

The correct option is A $0$
Using the formula for mth term, we get
$a_{m} = a_{1} + (m - 1) d$
Hence
$a_{1} + (m - 1) d = n$ ...(i)
Similarly
$a_{1} + (n - 1) d = m$ ...(ii)

Subtracting (ii) from (i)
$d (m - 1 - n + 1) = n - m$
$d (m - n) = n - m$
$d = - 1$ .

$a_{1} + (m - 1) (- 1) = n$

$a_{1} - m + 1 = n$

$a_{1} = m + n - 1$
Hence $(m + n)^{t h}$ term is
$a_{m + n} = a_{1} + (m + n - 1) d$
$= (m + n - 1) - (m + n - 1)$
$= 0$ .

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