- In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.
$$f ( x ) = \left( 2 + \frac { k x } { 8 } \right) ^ { 7 } \quad \text { where } k \text { is a non-zero constant }$$
- Find the first 4 terms, in ascending powers of \(x\), of the binomial expansion of \(\mathrm { f } ( x )\). Give each term in simplest form.
Given that, in the binomial expansion of \(\mathrm { f } ( x )\), the coefficients of \(x , x ^ { 2 }\) and \(x ^ { 3 }\) are the first 3 terms of an arithmetic progression,
- find, using algebra, the possible values of \(k\).
(Solutions relying entirely on calculator technology are not acceptable.)