Sequence And Series Question 179
Question: Three numbers are in G.P. such that their sum is 38 and their product is 1728. The greatest number among them is
[UPSEAT 2004]
Options:
A) 18
B) 16
C) 14
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let three number of G.P. i.e., $ a,,ar,,ar^{2} $ $ a+ar+ar^{2}=38 $ and $ a^{3}r^{3}=1728 $ ?..(i) $ a(1+r+r^{2})=38 $ ?..(ii) From equation (i) $ ar=12 $
Þ $ a=\frac{12}{r} $ From equation (ii) $ \frac{12}{r}(1+r+r^{2})=38 $ on solving $ r=2/3 $ and $ a=\frac{12\times 3}{2}=18 $ Required number 18, 12, 8 Maximum number i.e., 18.
BETA
