Question

In an A.P. the $p^{th}$ term is q and $q^{th}$ term is p, then its $r^{th}$ terms is

• A. p-q+r
• B. p+q+r
• C. p+q-r
• D. p-q-r

Answer 1

The correct option is C p+q-r

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

$(p-1)d-q=(q-1)d-p$

$pd-d-q=qd-d-p$

$d(p-q)=q-p$
$\Rightarrow d=-1$ and $a=q+p-1$

$t_r=a+(r-1)d=(q+p-1)+(r-1)(-1)=q+p-r$