Question

In the expansion of $(1+ax{)}^n$, the first three terms are $1+12x+64x^2$, then n=

• A. 16
• B. 18
• C. 20
• D. 9

Answer 1

The correct option is D

9

$(1+ax{)}^n$ = 1 + nax + $\frac{n(n-1)}{2}{a}^2{x}^2+..........$

Given nax = 12x and $\frac{n(n-1)}{2}{a}^2{x}^2=64x^2$

So $n^2{a}^2{x}^2$ - n$a^2{x}^2$ = 128 $x^2$ ⇒ 144 $x^2$ - $n{a}^2{x}^2$ = 128 $x^2$ ⇒ $n{a}^2{x}^2=16x^2$

So n = 9