Question

If the $A.M.$ between $p^{th}$ and $q^{th}$ terms of an $A.P.$ is equal to the $A.M.$ between $r^{th}$ and $s^{th}$ terms of the $A.P.$, then which of the following is true

• A. $p+q=r+s$
• B. $pq=rs$
• C. $pr=qs$
• D. $p+r=q+s$

Answer 1

The correct option is A $p+q=r+s$

Given $\frac{1}{2}(t_p+t_q)=\frac{1}{2}(t_r+t_s)\Rightarrow a+(p-1)d+a+(q-1)d=a+(r-1)d+a+(s-1)d\Rightarrow (p-1+q-1)d=(r-1+s-1)d\Rightarrow p+q=r+s$