Question

In an arithmetic progression, $T_m=nand{T}_n=m$, then $T_p=$

• A. $m+n-p$
• B. $m+n$
• C. $mn+p$
• D. $m^2+n^2{p}^2$

Answer 1

The correct option is A $m+n-p$

Let '$a$' be the first term and '$d$' be common difference of the A.P
$\Rightarrow T_m=a+(m-1)d=n\Rightarrow a-d=n-md...\left(1\right)$
and $T_n=a+(n-1)d=m\Rightarrow a-d=m-nd..\left(2\right)$
Using (1) and (2) we get, $d=-1$ and $a=n+m-1$
$\therefore T_p=a+(p-1)=n+m-1+(p-1)(-1)=n+m-p$
Hence, option 'A' is correct.