Question

In the expansion of $(1+x{)}^n$ the binomial coefficient of three consecutive terms are respectively 220,495 and 792. Find the value of n

Answer 1

Let the successive terms be $T_{r-1},T_r,T_{r+1}$ whose coefficient are 220 , 495 , and 792 respectively

$\frac{C_r}{C_{r-1}}=\frac{n-r+1}{r}$
$\therefore \frac{n-r+1}{r}=\frac{495}{220}=\frac{9}{4}$
$\therefore 4n-13r+4=0$

$\frac{C_{r+1}}{C_r}=\frac{n-r}{r+1}$

$\therefore \frac{n-r}{r+1}=\frac{792}{495}=\frac{8}{5}$

$\therefore 5n-13r-8=0$

$n=12$
$\therefore r=4$