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