Question

If the \((2p)^{\text{th}}\) term of a H.P. is \(q\) and the \((2q)^{\text{th}}\) term is \(p\), then the \(2(p+q)^{\text{th}}\) term is:

• A. \(\dfrac{pq}{2(p+q)}\)
• B. \(\dfrac{2pq}{p+q}\)
• C. \(\dfrac{pq}{p+q}\)
• D. \(\dfrac{p+q}{pq}\)

Hint:

H.P. problems are best solved by converting to A.P.

Answer 1

The Correct Option is C

Step 1: Convert H.P. to corresponding A.P. of reciprocals.
Step 2: Use linearity of A.P. terms.
Step 3: Required term equals harmonic mean: \[ T=\frac{pq}{p+q} \]