If the $p^{ ext {th }}$ term of an HP be $q$, and the $q^{ ext {th }}$ term be ' $p$ ', then the $

Question

If the $p^{	ext {th }}$ term of an HP be $q$, and the $q^{	ext {th }}$ term be ' $p$ ', then the $(p+q)^{	ext {th }}$ term is

Professor PC Thomas Classes · Answer

Let a be the first term and d the C.D. of the reciprocal AP. Then $ \  \begin{aligned} & \frac{1}{q}=a+(p-1) d \ & \frac{1}{p}=a+(q-1) d \Rightarrow \alpha=\frac{1}{p q}, d=\frac{1}{p q} \end{aligned} $