Sequence And Series Question 441
Question: What is the product of first 2n + 1 terms of a geometric progression?
Options:
A) The (n + 1)th power of the nth term of the GP
B) The (2n + 1)th power of the nth term of the GP
C) The (2n + 1)th power of the (n + 1)th term of the GP
D) The nth power of the (n + 1)th terms of the GP
Show Answer
Answer:
Correct Answer: C
Solution:
[c] The GP is a, $ ar,ar^{2},……ar^{2n} $ So, $ P=a.,ar..ar^{2}.ar^{3}……..ar^{2n} $ $ ={a^{2n+1}}.{r^{1+2+……+2n}} $ $ ={a^{(2n+1)}}r,{{,}^{\frac{2n(2n+1)}{2}}}={a^{2n+1}}{r^{n(2n+1)}}={{(ar^{n})}^{(2n+1)}} $ $ =(2n+1)th $ power of the $ (n+1)th $ term of GP.
BETA
