If the coefficients of three consecutive terms in the expansion of ${(1 + x)}^n$ are in the ratio $1 : 7 : 42$, then value of $n$ is

Let three consecutive terms be $(r + 1)$th, $(r + 2)$th and $(r + 3)$th. Then
       $\frac{{ }^n{C}_r}{{ }^n{C}_{r+1}}=\frac{1}{7}\Rightarrow \frac{r+1}{n-r}=\frac{1}{7}\Rightarrow n-8r=7$
and $\frac{{ }^n{C}_{r+1}}{{ }^n{C}_{r+2}}=\frac{7}{42}=\frac{1}{6}\Rightarrow \frac{r+2}{n-r-1}=\frac{1}{6}$

$\Rightarrow n-7r=13$|
From $\left(1\right)$ and $\left(2\right), n=55.$