Question

In an $A.P$., if $m^{th}$ term is $n$ and the $n^{th}$ term is $m$, where $m \ne n$, then find its $p^{th}$ term.

• A. $ n - m + p$
• B. $n + m + p $
• C. $n + m -p$
• D. $ n - m - p$

Answer 1

Answer: (C)

We have, $a_{m} = a + \left(m - 1\right)d = n\quad....\left(i\right)$
and $a_{n} = a + \left(n - 1\right)d = m \quad....\left(ii\right)$
Solving $\left(i\right)$ and $\left(ii\right)$, we get
$\left(m - n\right)d = n-m$
$ \Rightarrow d = -1$
and so, $a = n + m - 1 $
Now, $a_{p }= a + \left(p-1\right)d $
$= n + m- 1 + \left(p- 1\right)\left(-1\right)$
$ = n + m -p $