Sequence And Series Question 424
The value of x + y + z is 15 if a, x, y, z, b are in A.P. while the value of $ \frac{1}{x}+\frac{1}{y}+\frac{1}{z} $ is $ \frac{5}{3} $ if a, x, y, z, b are in G.P. Then the value of a and b are
Options:
A) 2 and 8
B) 1 and 9
C) 3 and 7
D) None
Show Answer
Answer:
Correct Answer: B
Solution:
As x, y, z are A.M. of a and b
$ \therefore ,x+y+z=3( \frac{a+b}{2} ) $
$ \therefore ,15=\frac{3}{2}(a+b)\Rightarrow a+b=10 $ ??. (1) Again $ \frac{1}{x},\frac{1}{y},\frac{1}{z} $ are H.M. of $ \frac{1}{a} $ and $ \frac{1}{b} $
$ \therefore \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{3}{2},( \frac{1}{a}+\frac{1}{b} ) $
$ \therefore \frac{5}{3}=\frac{3}{2} \cdot \frac{a+b}{ab} $
$ \Rightarrow ,\frac{10}{9}=\frac{10}{ab}\Rightarrow ab=9 $ ??.. (2) Solving equations (1) and (2), we get $ a=9,b=1,9 $
BETA
