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 integer m,n, `T_m=1/n` and `T_n=1/m` then `a-d=`
A. `(1)/(mn)`
B. `(1)/(m)+(1)/(n)`
C. 1
D. 0

Answer 1

Correct Answer - C
Let a be the term and d be the common difference of the given AP. Then,
`T_(m)=(1)/(n)rArra=(m+1)d=(1)/(n)` . . . (i)
`and,T_(n)=(1)/(m)rArra+(n-1)d=(1)/(m)` . . . (ii)
Solving (i) and (ii), we get `d=(1)/(mn)anda=(1)/(mn)`
`:." "T_(mn)=a+(mn-1)d=(1)/(mn-1)(1)/(mn)=1`