Sequence And Series Question 638
Question: If the $ m^{th} $ term of a H.P. be $ n $ and $ n^{th} $ be $ m $ , then the $ r^{th} $ term will be
Options:
A) $ \frac{r}{mn} $
B) $ \frac{mn}{r+1} $
C) $ \frac{mn}{r} $
D) $ \frac{mn}{r-1} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ T_{m}=n,\ T_{n}=m $ for H.P. Therefore for the corresponding A.P. $ m^{th} $ term $ =\frac{1}{n},\ n^{th} $ term $ =\frac{1}{m} $ Let $ a $ and d be the first term and common difference of this A.P., then $ a+(m-1)d=\frac{1}{n} $ ?..(i) $ a+(n-1)d=\frac{1}{m} $ ?..(ii) Solving these, we get $ a=\frac{1}{mn},\ d=\frac{1}{mn} $ Now, $ r^{th} $ term of corresponding A.P. $ =a+(r-1)d=\frac{1}{mn}+(r-1)\frac{1}{mn}=\frac{1+r-1}{mn}=\frac{r}{mn} $ Therefore $ r^{th} $ term of corresponding H.P. is $ \frac{mn}{r} $ . Note: Students should remember this question as a fact.
BETA
