Question

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

Answer 1

Let ${}^{\prime }{a}^{\prime }$ be the first term & ${}^{\prime }{d}^{\prime }$ be the common difference.

$n=a+(m-1)d$

$m=a+(n-1)d$

$n-m=(m-1)d-(n-1)d=(m-1-n+1)d$

$\Rightarrow d=-1$

$n=a-(m-1)$

$\Rightarrow a=n+m-1$

$\therefore$ $pth$ term $=(n+m-1)-p=m+n-p-1$

Hence, this is the answer.