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Question: Answered & Verified by Expert
Let $\mathrm{T}_{\mathrm{r}}$ be the $\mathrm{r}^{\text {th }}$ term of an AP for $\mathrm{r}=1,2,3, \ldots$. If for some distinct positive integers $\mathrm{m}$ and $\mathrm{n}$ we have $\mathrm{T}_{\mathrm{m}}=1 / \mathrm{n}$ and $\mathrm{T}_{\mathrm{n}}=1 / \mathrm{m}$, then what is $\mathrm{T}_{\mathrm{mn}}$ equal to?
MathematicsSequences and SeriesNDANDA 2018 (Phase 2)
Options:
  • A $(\mathrm{mn})^{-1}$
  • B $\mathrm{m}^{-1}+\mathrm{nn}^{-1}$
  • C 1
  • D 0
Solution:
2005 Upvotes Verified Answer
The correct answer is: 1
$\quad \mathrm{T}_{\mathrm{n}}=\frac{1}{m}, \mathrm{~T}_{\mathrm{m}}=\frac{1}{n}$
$\Rightarrow \quad 1^{\text {st }}$ term $=\mathrm{c.d}=\frac{1}{m n}$
$\Rightarrow \quad \mathrm{T}_{m n}=\frac{1}{m n}+\frac{m n-1}{m n}=1$

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