Question

The $p^{th}$ term of an arithmetic progression is $q$, and the $q^{th}$ term is $p$; then the $m^{th}$ term is:

• A. $p+q-m$
• B. $p-q-m$
• C. $p+q+m$
• D. None of these

Answer 1

The correct option is A $p+q-m$

Let the first term and the common difference of the A.P. be $a$ and $d$ respectively.

Then the $p$ th and $q$ th terms of the series are $a+(p-1)d$ and $a+(q-1)d$ respectively.

Then by the problem,

$a+(p-1)d=q$......(1) and $a+(q-1)d=p$.......(2).

Now (1)$-$(2) gives

$(p-q)d=q-p$

or, $d=-1$.

Using value of $d$ in (1) we get $a=p+q-1$.

Now, the $m$ th term of the A.P. will be $a+(m-1)d=p+q-m$ [ Using values of $a$ and $d$.]