Sequence And Series Question 589
Question: If the $ p^{th} $ , $ q^{th} $ and $ r^{th} $ term of a G.P. are $ a,\ b,\ c $ respectively, then $ {a^{q-r}}.\ {b^{r-p}}.\ {c^{p-q}} $ is equal to
[Roorkee 1955, 63, 73; Pb. CET 1991, 95]
Options:
A) 0
B) 1
C) $ abc $
D) $ pqr $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ a,\ b,\ c,\ d $ ?..(i) $ A{R^{q-1}}=b $ ?..(ii) and $ A{R^{r-1}}=c $ ?..(iii) So $ {a^{q-r}}{b^{r-p}}{c^{p-q}} $ $ ={{{ A{R^{p-1}} }}^{q-r}}{ A{R^{q-1}} }{{,}^{r-p}}{{{ A{R^{r-1}} }}^{p-q}} $ $ 12^{th} $ $ =A^{0}R^{0}=1 $ . Note: Such type of questions $ i.e. $ containing terms of powers in cyclic order associated with negative sign, reduce to 1 mostly.
BETA
