The initial phase of a biological growth process is modeled by the function B(t)=(2+κt4)7B(t) = \left( 2 + \frac{\kappa t}{4} \right)^7B(t)=(2+4κt)7, where ttt is the time in hours and κ\kappaκ is a non-zero constant.
Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of B(t)B(t)B(t). Give each term in simplest form.
Given that, in the binomial expansion of B(t)B(t)B(t), the coefficients of ttt, t2t^2t2 and t3t^3t3 are the first three terms of an arithmetic progression,
find, using algebra, the possible values of κ\kappaκ.
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.