Let T_r be the r-th term of an A.P.

Question

Let $T_r$ be the $r$-th term of an A.P. whose first term is $a$ and common difference is $d$. If for some positive integers $m,n$, $m
e n$, $T_m=\dfrac1n$ and $T_n=\dfrac1m$, then $a-d$ equals:

Accepted Answer

$a+(m-1)d=\dfrac1n$ ... (i); $a+(n-1)d=\dfrac1m$ ... (ii).

Subtracting: $(m-n)d=\dfrac1n-\dfrac1m=\dfrac{m-n}{mn}\Rightarrow d=\dfrac{1}{mn}$.

From (i): $a=\dfrac1n-(m-1)\dfrac{1}{mn}=\dfrac{m-(m-1)}{mn}=\dfrac{1}{mn}$.

So $a-d=0$.

Solutions · 1