Sequence And Series Question 359
Question: If S, P and R are the sum, product and sum of the reciprocals of n terms of an increasing GP respectively and $ S^{n}=R^{n}.P^{k}, $ then k is equal to
Options:
A) 1
B) 2
C) 3
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ S=\frac{a(1-r^{n})}{1-r},P=a^{n}.{r^{\frac{n(n-1)}{2}}} $ $ R=\frac{1}{a}+\frac{1}{ar}+\frac{1}{ar^{2}}+…..nterms=\frac{1-r^{n}}{a(1-r){r^{n-1}}} $ $ S^{n}=R^{n}P^{k}\Rightarrow {{( \frac{S}{R} )}^{n}}=P^{k} $
$ \Rightarrow {{(a^{2},{r^{n-1}})}^{n}}=P^{k}\Rightarrow P^{2}=P^{k}\Rightarrow k=2 $
BETA
