Question

If $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$, then $10^{th}$ term is

• A. $p-q+10$
• B. $p+q+11$
• C. $p+q-9$
• D. $p+q-10$

Answer 1

Answer: (D)

$p+q-10$

Answer 2

Let first term and common difference of an AP be a and d. According to the question,
${{T}_{p}}=a+(p-1)d$
$\Rightarrow$ $q=a+(p-1)d$ ..(i)
and ${{T}_{q}}=a+(q-1)d$
$\Rightarrow$ $p=a+(q-1)d$ ..(ii)
On solving Eqs. (i) and (ii), we get
$d=-1$ and $a=p+q-1$
$\therefore$ ${{T}_{10}}=a+(10-1)d=p+q-10$