Let T_r be the rth term of an A.P.

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, $$m \ne n,\,\,{T_m} = {1 \over n}\,\,and\,{T_n} = {1 \over m},\,$$ then a - d equals

Accepted Answer

$${T_m} = a + \left( {m - 1} \right)d = {1 \over n}...........\left( 1 \right)$$

$${T_n} = a + \left( {n - 1} \right)d = {1 \over m}..........\left( 2 \right)$$

$$\left( 1 \right) - \left( 2 \right) \Rightarrow \left( {m - n} \right)d$$

$$ = {1 \over n} - {1 \over m} \Rightarrow d = {1 \over {mn}}$$

From $$\left( 1 \right)$$ $$a = {1 \over {mn}} \Rightarrow a - d = 0$$

Solutions · 1