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Nth Term of GP

Let T r be th...

Question

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

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Solution

The correct option is A
$T_{m} = a + (m - 1) d = \frac{1}{n}, T_{n} = a + (n - 1) d = \frac{1}{m} S u b s t r a c t i n g (m - n) d = \frac{1}{m n}, a = \frac{1}{n} - \frac{1}{m} = \frac{m - n}{m} \Rightarrow d = \frac{1}{m n}, a = \frac{1}{n} - \frac{(m - 1)}{m n} = \frac{1}{m n} ∴ a - d = 0$

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$n, m \neq n, T_{m} = \frac{1}{n}, T_{n} = \frac{1}{m}$ then a – d =

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