Question

Let $T_r$ be the rth term of an A.P. whose first term is $a$, and common difference is $d$. If for some positive integers $m,n$, $T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then $a-d=$

• A. $0$
• B. $\frac{1}{m}+\frac{1}{n}$
• C. $\frac{1}{mn}$
• D. $1$

Answer 1

Answer: (A)

$0$

$T_m=1/n=a+(m-1)d$ ..............(I)
$T_n=1/m=a+(n-1)d$ ................(II)
then, (I)-(II) gives
$(m-n)d=(m-n)/mn$
$\Rightarrow d=1/mn$
from (I), $1/n=a+(m-1)/mn$
$\Rightarrow m+1=amn+m$
$\Rightarrow a=1/mn$
then, $a-d=0$