The volume of a growing tropical fruit, V(x)V(x)V(x) in cm3\text{cm}^3cm3, after x x\,x weeks is modeled by the function
V(x)=(2+kx4)7V(x) = \left(2 + \frac{kx}{4}\right)^7V(x)=(2+4kx)7
where k k\,k is a non-zero constant.
Find the first 4 terms, in ascending powers of xxx, of the binomial expansion of V(x)V(x)V(x). Give each term in simplest form.
Given that the coefficients of xxx, x2x^2x2, and x3 x^3\,x3 in this expansion form the first three terms of an arithmetic progression,
find, using algebra, the possible values of kkk.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.