Question

The first 3 terms in the expansion of $(1+ax{)}^n$ (n ≠ 0) are 1, 6x and 16$x^2$. Then the value of a and n are respectively

• A. 2 and 9
• B. 3 and 2
• C. $\frac{2}{3}$ and 9
• D. $\frac{3}{2}$ and 6

Answer 1

The correct option is C

$\frac{2}{3}$ and 9

$n_{c_1}.ax=6x;n_{c_2}(ax{)}^2=16x^2\Rightarrow an=6;\frac{n(n-1)}{2}{a}^2=16\Rightarrow a=\frac{2}{3}\Rightarrow n=9$