- The first three terms, in ascending powers of \(x\), of the binomial expansion of \(( 1 + k x ) ^ { 16 }\) are
$$1 , - 4 x \text { and } p x ^ { 2 }$$
where \(k\) and \(p\) are constants.
- Find, in simplest form,
- the value of \(k\)
- the value of \(p\)
$$g ( x ) = \left( 2 + \frac { 16 } { x } \right) ( 1 + k x ) ^ { 16 }$$
Using the value of \(k\) found in part (a),
- find the term in \(x ^ { 2 }\) in the expansion of \(\mathrm { g } ( x )\).
$$\begin{aligned}
u _ { 1 } & = 6
u _ { n + 1 } & = k u _ { n } + 3
\end{aligned}$$
where \(k\) is a positive constant. - Find, in terms of \(k\), an expression for \(u _ { 3 }\)
Given that \(\sum _ { n = 1 } ^ { 3 } u _ { n } = 117\)
- find the value of \(k\).