A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by u1=3u_1 = 3u1=3 and un+1=un+c,n≥1u_{n+1} = u_n + c, \quad n \geq 1un+1=un+c,n≥1.
Find the value of c c\,c given u5=21u_5 = 21u5=21.
Find an expression for un u_n\,un in terms of nnn.
178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.