Let Tr be the rth term of an A-P- for r- N- If for some positive integers m and n- we have Tm-1n and Tn-1m- then Tmn is equal to

Let $T_{r}$ be the $r^{t h}$ term of an A.P, for r=1, 2, 3,-------. If for some positive integers m,n we have $T_{m} = \frac{1}{n}$ and $T_{n} = \frac{1}{m}$ , then $T_{m n}$ =

Q. Let

T_{r}

be the

r^{t h}

term of an A.P., for

r = 1, 2, . . .

If for some positive integers

m

and

n, T_{m} = \frac{1}{n}; T_{n} = \frac{1}{m}

then find

T_{m n}

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Let Tr be the rth term of an A.P. for r∈N. If for some positive integers m and n, we have Tm=1n and Tn=1m, then Tmn is equal to

The correct option is C 1It is given that tm=1n and tn=1m i.e., a+(m−1)d=1na+(n−1)d=1mSubtracting both, we get:(m−n)d=1n−1mThus, d=1mnSubstitute, d=1mn to get, a=1mn.Thus, tmn=a+(mn−1)d=1

Let $T_{r}$ be the $r^{t h}$ term of an A.P. for $r \in N$ . If for some positive integers $m$ and $n$ , we have $T_{m} = \frac{1}{n}$ and $T_{n} = \frac{1}{m}$ , then $T_{m n}$ is equal to