question_answer

Let\[{{T}_{r}}\]be the rth term of an AP whose first term is a and common difference is d. If for some positive integers \[m,n,m\ne n,{{T}_{m}}=\frac{1}{n}\]and\[{{T}_{n}}=\frac{1}{m},\]then\[a-d\]equals

A) 0     

B)                       1             

C)        \[\frac{1}{mn}\]              

D)        \[\frac{1}{m}+\frac{1}{n}\]

Correct Answer: A

Solution :

Given that,                                      ...(i) and                                           ...(ii) On solving Eqs. (i) and (ii), we get and