Binomial Expansion

The volume of a growing tropical fruit, $V (x)$ in $cm3\text{cm}^3$ , after $x\,$ weeks is modeled by the function

\left(2 + \frac{kx}{4}\right)^7

where $k\,$ is a non-zero constant.

Find the first 4 terms, in ascending powers of $x$ , of the binomial expansion of $V (x)$ . Give each term in simplest form.

[4]

Given that the coefficients of $x$ , $x^2$ , and $x^3\,$ in this expansion form the first three terms of an arithmetic progression,

find, using algebra, the possible values of $k$ .

[4]

Binomial Expansion Questions

The volume of a growing tropical fruit, $V (x)$ in $cm3\text{cm}^3$ , after $x\,$ weeks is modeled by the function

\left(2 + \frac{kx}{4}\right)^7

where $k\,$ is a non-zero constant.

Find the first 4 terms, in ascending powers of $x$ , of the binomial expansion of $V (x)$ . Give each term in simplest form.

[4]

Given that the coefficients of $x$ , $x^2$ , and $x^3\,$ in this expansion form the first three terms of an arithmetic progression,

find, using algebra, the possible values of $k$ .

[4]