Question

If the $p^{th}$ term of an AP is $q$ and its $q^{th}$ term is $p$, then its $(p+q{)}^{th}$ term is

• A. $p$
• B. $q$
• C. $(p+q)$
• D. $0$

Answer 1

Answer: (D)

$0$

By using nth term $t_n=a+(n-1)d$ we have,

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

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

Solving (1) and (2), we get

$d=-1,a=p+q-1$

$\therefore T_{p+q}=a+(p+q-1)d$

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

$=p+q-1-p-q+1$

$=0$