First slide

Arithmetic progression

Question

$Let T_{r} be the r^{th} term of an A.P. whose first term is a and common$ $difference is d . If for some positive integers m, n, m \neq n, T_{m} = \frac{1}{n} and T_{n} = \frac{1}{m},$ $then a-d$

Moderate

A

0
B

$\frac{1}{m} + \frac{1}{n}$
C

$\frac{1}{m n}$
D

1

Solution

$T_{m} = a + (m - 1) d = \frac{1}{n}, T_{n} = a + (n - 1) d = \frac{1}{m}$
$Solving a = \frac{1}{m n} a n d d = \frac{1}{m n} \Rightarrow a - d = 0$

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