Question

In an AP, the $p^{th}$ term is $q$ and the $(p+q{)}^{th}$ term is $0$. Then the $q^{th}$ term is

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

Answer 1

The correct option is B $p$

We have,

$a+(p-1)d=q$ ........(1)
Also,

$a+(p+q-1)d=0$

$\Rightarrow a+(p-1)d+qd=0$

$\Rightarrow q+qd=0\Rightarrow d=-1(\because q\ne 0)$

$q^{th}$ term $=a+(q-1)d=a-q+1$

From (1), $a+(p-1)(-1)=q\Rightarrow a-q+1=p$

$\therefore q^{th}$ term$=p$
Hence, option B is correct