Question

If the $m^{th}$ term and the $n^{th}$ term of an AP are respectively $\frac{1}{n}$ and $\frac{1}{m}$, then the $m{n}^{th}$ term of the AP is

• A. $\frac{1}{mn}$
• B. $\frac{m}{n}$
• C. $1$
• D. $\frac{n}{m}$

Answer 1

The correct option is C $1$

Let a and d be the first term and common difference of an AP.
Since, $T_m=\frac{1}{n}$
$\therefore a+(m-1)d=\frac{1}{n}$....(i)
and $T_n=\frac{1}{m}$
$\Rightarrow a+(n-1)d=\frac{1}{m}$.....(ii)
On solving Eqs. (i) and (ii), we get
$a=\frac{1}{mn}$ and $d=\frac{1}{mn}$
$\therefore T_{mn}=a+(mn-1)d$

$=\frac{1}{mn}+\frac{(mn-1)}{mn}$

$=\frac{mn}{mn}=1$