A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by
u1=3u_1 = 3u1=3
un+1=un+cu_{n+1} = u_n + cun+1=un+c, n≥1 n \geq 1\,n≥1
where c c\,c is a constant.
It is given that u5=23u_5 = 23u5=23.
Find the value of ccc.
Find an expression for un u_n\,un in terms of nnn.
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.