Question

$(p+q{)}^{th}$ and $(p-q{)}^{th}$ terms of an A.P. are respectively $m$ and $n.$ The $p^{th}$ term is

• A. $\frac{1}{2}(m+n)$
• B. $\sqrt{mn}$
• C. $m+n$
• D. $mn$

Answer 1

The correct option is A $\frac{1}{2}(m+n)$

Let $a$ be the first term and $d$ be the common difference of the given $AP$ then, by using $n^{th}$ term formula

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

$(p+q{)}^{th}=m\Rightarrow a+(p+q-1)d=m$ ...(1)

$(p-q{)}^{th}=n\Rightarrow a+(p-q-1)d=n$ ...(2)

Adding (1) and (2), we get

$2a+(2p-2)d=m+n$

$\Rightarrow a+(p-1)d=\frac{m+n}{2}$

$\Rightarrow p^{th}term=\frac{m+n}{2}$

So, Option A is correct.