Sequence And Series Question 594
Question: If $ a,\ b,\ c $ are $ p^{th},\ q^{th} $ and $ r^{th} $ terms of a G.P., then $ {{( \frac{c}{b} )}^{p}}{{( \frac{b}{a} )}^{r}}{{( \frac{a}{c} )}^{q}} $ is equal to
Options:
A) 1
B) $ a^{P}b^{q}c^{r} $
C) $ a^{q}b^{r}c^{p} $
D) $ a^{r}b^{p}c^{q} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ a=A{R^{p-1}},\ b=A{R^{q-1}},\ c=A{R^{r-1}} $
$ \therefore $ $ {{( \frac{c}{b} )}^{p}}{{( \frac{b}{a} )}^{r}}{{( \frac{a}{c} )}^{q}}={{( \frac{A{R^{r-1}}}{A{R^{q-1}}} )}^{p}}{{( \frac{A{R^{q-1}}}{A{R^{p-1}}} )}^{r}}{{( \frac{A{R^{p-1}}}{A{R^{r-1}}} )}^{q}} $ $ ={R^{(r-q)p+(q-p)r+(p-r)q}}=R^{0}=1 $ .
BETA
