Answer:
Option C
Explanation:
Let the three consecutive terms in (1+x) n+5 be tr , tr+1, tr+2 . Having coefficients
$^{n+5}C_{r-1},^{n+5}C_{r}, ^{n+5}C_{r+1}$ given, $^{n+5}C_{r-1}:^{n+5}C_{r}: ^{n+5}C_{r+1}$ =5:10:14
$\frac{^{n+5}C_{r}}{^{n+5}C_{r-1}}=\frac{10}{5}$
and $\frac{^{n+5}C_{r+1}}{^{n+5}C_{r}}=\frac{14}{10}$
$\Rightarrow$ $\frac{n+5-(r-1)}{r}=2$
and $\frac{n-r+5}{r+1}=\frac{7}{5}$
$\Rightarrow$ n-r+6=2r
and 5n-5r+25=7r+7
$\Rightarrow$ n+6=3r
and 5n+18=12 r
$\therefore$ $\frac{n+6}{3}=\frac{5n+18}{12}$
$\Rightarrow$ 4n+24=5n+18
$\Rightarrow$ n=6
