Sequence And Series Question 313
Question: In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number, the series becomes A.P., then the greatest number is
[Roorkee 1973]
Options:
A) 8
B) 4
C) 24
D) 16
Show Answer
Answer:
Correct Answer: A
Solution:
Let three numbers in G.P. are $ \frac{a}{r},\ a,\ ar $ . Condition I: $ \frac{a}{r}+a+ar=14\Rightarrow a( \frac{1}{r}+1+r )=14 $ ?.(i) Condition II: $ \frac{a}{r}+1,\ a+1 $ and $ ar-1 $ will be in A.P., then $ 2(a+1)=\frac{a}{r}+1+ar-1=\frac{a}{r}(1+r^{2}) $ ……(ii) From (i) and (ii), we get $ a=4 $ and $ r=2 $ . So, required numbers are 2, 4, 8. Hence greatest number is 8.
BETA
