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Question: Answered & Verified by Expert
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 $m, n, m \neq n, T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then $a-d$ equals
MathematicsSequences and SeriesJEE MainJEE Main 2004
Options:
  • A
    0
  • B
    1
  • C
    $\frac{1}{\mathrm{mn}}$
  • D
    $\frac{1}{m}+\frac{1}{n}$
Solution:
1476 Upvotes Verified Answer
The correct answer is:
0
$$
T_m=\frac{1}{n}=a+(m-1) d
$$
and $T_n=\frac{1}{m}=a+(n-1) d$
from (1) and (2) we get $a=\frac{1}{m n}, \quad d=\frac{1}{m n}$ Hence $\mathrm{a}-\mathrm{d}=0$

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