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)

$n + m -p$

Answer 2

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, $a_{p }= a + \left(p-1\right)d$ $= n + m- 1 + \left(p- 1\right)\left(-1\right)$ $= n + m -p$