Sequence And Series Question 10
Question: In a H.P., pth term is q and the qth term is p. Then pqth term is
[Karnataka CET 2002]
Options:
A) 0
B) 1
C) pq
D) $ pq(p+q) $
Show Answer
Answer:
Correct Answer: B
Solution:
Let a be the first term and d be the common difference of the corresponding A.P. $ p^{th} $ term of A.P. $ (T_{p})=a+(p-1)d=\frac{1}{q} $ ?..(i) $ q^{th} $ term of A.P. $ (T_{q})=a+(q-1)d=\frac{1}{p} $ ?..(ii) From (i) - (ii), $ (p-q)d=\frac{1}{q}-\frac{1}{p}=\frac{p-q}{pq}\Rightarrow ,d=\frac{1}{pq} $ From (i), $ a+(p-1)\frac{1}{pq}=\frac{1}{q} $
Þ $ a=\frac{1}{pq} $ . \ $ T_{pq}=a+(pq-1)d=\frac{1}{pq}+(pq-1)\frac{1}{pq}=1 $ . Therefore $ pq^{th} $ term is 1.
BETA
