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 $m, n, m ≠ n,$ $T_{m} = \frac{1}{n}$ and $T_{n} = \frac{1}{m},$ then $a - d$ equals

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

Answer 1

Answer: (A)

$T_{m} = \frac{1}{n} = a+\left(m-1\right)d\quad\quad.....\left(1\right)$
and $T_{n} = \frac{1}{m} = a+\left(n-1\right)d\quad \quad .....\left(2\right)$
from $\left(1\right)$ and $\left(2\right)$ we get $a = \frac{1}{mn}, d = \frac{1}{mn}$
Hence $a - d = 0$