Sequence And Series Question 345
Question: If the pth term of an A.P. $ be\frac{1}{q} $ and qth term be $ \frac{1}{p}, $ then the sum of its pqth terms will be
Options:
A) $ \frac{pq-1}{2} $
B) $ \frac{1-pq}{2} $
C) $ \frac{pq+1}{2} $
D) $ -\frac{pq+1}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Since $ T_{p}=a+(p-1)d=\frac{1}{q}….(i) $ and $ T_{q}=a+(q-1)d=\frac{1}{p}….(ii) $ From (i) and (ii), we get $ a=\frac{1}{pq} $ and $ d=\frac{1}{pq} $ Now sum of pq terms $ =\frac{pq}{2}[ \frac{2}{pq}+(pq-1)\frac{1}{pq} ] $ $ =\frac{pq}{2}.\frac{2}{pq}[ 1+\frac{1}{2}(pq-1) ]=[ \frac{2+pq-1}{2} ]=\frac{pq+1}{2} $
BETA
