Sequence And Series Question 614
Question: Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4, then
[IIT Screening 2000; DCE 2001]
Options:
A) $ a=\frac{7}{4},,r=\frac{3}{7} $
B) $ a=\frac{3}{2},,r=\frac{1}{2} $
C) $ a=2,,r=\frac{3}{8} $
D) $ a=3,,r=\frac{1}{4} $
Show Answer
Answer:
Correct Answer: D
Solution:
Here $ \frac{a}{1-r}=4andar=\frac{3}{4} $ . Dividing these, $ r(1-r)=\frac{3}{16} $ or $ 16r^{2}-16r+3=0 $ or $ (4r-3)(4r-1)=0 $ $ r=\frac{1}{4},\frac{3}{4}\text{and }a=3,,1 $ so $ (a,r)=( 3,\frac{1}{4} ),,,( 1,\frac{3}{4} ) $ .
BETA
