A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by
u1=8un+1=un+k,n≥1 \begin{aligned}u_1 &= 8 \\u_{n+1} &= u_n + k, \quad n \geq 1\end{aligned} u1un+1=8=un+k,n≥1Given u5=32u_5 = 32u5=32
Find the value of kkk.
Find an expression for un u_n\,un in terms of nnn.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) 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.
