Question

If pth term of a HP is qr and its qth term is pr,then its rth term is.

• A. pq
• B. $\frac{1}{pq}$
• C. $\frac{1}{pqr}$
• D. pqr

Answer 1

The correct option is A pq

pth term of a HP is qr and its qth term is pr.
$\Rightarrow \frac{1}{a+(p-1)d}=qr$$\Rightarrow a+(p-1)d=\frac{1}{qr}$ ----(1)
$\Rightarrow \frac{1}{a+(q-1)d}=pr$$\Rightarrow a+(q-1)d=\frac{1}{pr}$ ----(2)
(1)-(2) gives
$d(p-q)=\frac{p-q}{pqr}$
$d=\frac{1}{pqr}$
from (1)
$a=\frac{1}{qr}-\frac{p-1}{pqr}$
$a=\frac{1}{pqr}$
$\therefore a+(r-1)d=\frac{1}{pqr}+\frac{r-1}{pqr}=\frac{1}{pq}$
$\therefore$ rth term of HP is $pq$
Hence, option A.