Let T_{r} be the r^{{th}{~}} term of an A.P. for r ... | Sequence & Series (Mathematics)

Let

T_{r}

be the

r^{\text{th}\text{~}}

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_{mn}

equals

\frac{1}{mn}

\frac{1}{m}+\frac{1}{n}

Correct Answer:

\begin{aligned}& \text { (c) }: T_m=a+(m-1) d=\frac{1}{n} \\& T_n=a+(n-1) d=\frac{1}{m} \\& \text { or }(m-n) d=\frac{1}{n}-\frac{1}{m}=\frac{(m-n)}{m n} \text { or } d=\frac{1}{m n} \\& \text { Now, } T_{m n}=a+(m n-1) d \\& =a+(n-1) d+(m n-n) d \\& =\frac{1}{m}+\frac{1}{m n} n(m-1)=1\end{aligned}

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