Sequence And Series Question 366
Question: If the coefficients of rth, (r + 1)th, and (r + 2)th terms in the binomial expansion of $ {{(1+y)}^{m}} $ are in A.P, then m and r satisfy the equation
Options:
A) $ m^{2}-m( 4r-1 )+4r^{2}-2=0 $
B) $ m^{2}-m( 4r+1 )+4r^{2}+2=0 $
C) $ m^{2}-m(4r+1)+4r^{2}-2=0 $
D) $ m^{2}-m( 4r-1 )+4r^{2}+2=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Given $ ^{m}{C_{r-1}},{{,}^{m}}C_{r},{{,}^{m}}{C_{r+1}} $ are in A.P. $ 2^{m}C_{r}={{,}^{m}}{C_{r-1}}+{{,}^{m}}{C_{r+1}} $
$ \Rightarrow 2=\frac{^{m}{C_{r-1}}}{^{m}C_{r}}+\frac{^{m}{C_{r+1}}}{^{m}C_{r}}=\frac{r}{m-r+1}+\frac{m-r}{r+1} $
$ \Rightarrow m^{2}-m(4r+1)+4r^{2}-2=0 $ .
BETA
