Given that $(1+ax)^n=1-12x+63x^2+\ldots+a^nx^n$, where $n\in\mathbb{Z}^+$, find the values of \(

Question

Given that $(1+ax)^n=1-12x+63x^2+\ldots+a^nx^n$, where $n\in\mathbb{Z}^+$, find the values of $a$ and $n$, the term containing $x^5$.

Accepted Answer

$a=-\frac32$, $n=8$; the term is $-\frac{1701}{4}x^5$.

IB Math HL January 2016 P2 Q2