A quantitative analyst models the projected value of a portfolio using the function
V(x)=(4+kx)7V(x) = (4 + kx)^7V(x)=(4+kx)7
where x x\,x represents market volatility and k k\,k is a positive constant.
Find the first three terms, in ascending powers of xxx, in the expansion of (4+kx)7(4 + kx)^7(4+kx)7, giving each term in its simplest form.
Given that the coefficient of x2 x^2\,x2 is exactly three-eighths of the coefficient of xxx, determine the value of kkk.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.