A quantitative analyst models the projected value of a high-risk portfolio using the function V(x)=(4+kx)7V(x) = (4 + kx)^7V(x)=(4+kx)7, where xxx represents market volatility and kkk is a positive sensitivity constant.
Find the first three terms, in ascending powers of xxx, in the expansion of
(4+kx)7 (4 + kx)^7 (4+kx)7giving each term in its simplest form.
Given that the coefficient of x2x^2x2 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.