Sequence And Series Question 258
Question: If the $ p^{th} $ term of an A.P. be $ \frac{1}{q} $ and $ q^{th} $ term be $ \frac{1}{p} $ , then the sum of its $ pq^{th} $ 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:
Since $ T_{p}=a+(p-1)d=\frac{1}{q} $ ?..(i) ……(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} $ Note: Students should remember this question as a formula.
BETA
