If the A.M.

Question

If the A.M. between the $p$-th and $q$-th terms of an A.P. is equal to the A.M. between the $r$-th and $s$-th terms of the same A.P., then $p+q$ is equal to:

Accepted Answer

$$\frac{a_p+a_q}{2}=\frac{a_r+a_s}{2} \Rightarrow [a+(p-1)d]+[a+(q-1)d]=[a+(r-1)d]+[a+(s-1)d]$$
$$\Rightarrow 2a+(p+q-2)d=2a+(r+s-2)d \Rightarrow (p+q)d=(r+s)d \Rightarrow p+q=r+s.$$

Solutions · 1