Sequence And Series Question 624
Question: If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is
[Roorkee 1972]
Options:
A) $ -\frac{3}{2} $
B) $ \frac{3}{2} $
C) 2
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
Let three terms of G.P. are $ a,\ ar,\ ar^{2} $ . Then $ a+ar+ar^{2}=19\Rightarrow a[1+r+r^{2}]=19 $ ?..(i) $ a\ .\ ar\ .\ ar^{2}=216\Rightarrow a^{3}r^{3}=216\Rightarrow ar=6 $ ?..(ii) Dividing (ii) by (i), $ \frac{6}{r}+\frac{6}{r}r+\frac{6}{r}r^{2}=19\Rightarrow \frac{6}{r}+6+6r=19 $
$ \Rightarrow r^{2}-\frac{13}{6}r+1=0 $ . Hence $ r=\frac{3}{2} $ .
BETA
