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.
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.