A-level · Sequences & series

Sigma notation and recurrence relationsExam-style questions

Reading and evaluating sums written with Σ, and generating sequences from a recurrence relation — including spotting periodic behaviour.

27 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

1
Evaluate $\displaystyle\sum_{r=1}^{10} (2r + 1)$ .
Level 3 · 2 marksTry it
2
A sequence is defined by $u_{n+1} = 2u_n - 1$ with $u_1 = 3$ . Find $u_2$ , $u_3$ and $u_4$ .
Level 3 · 2 marksTry it
3
Evaluate $\displaystyle\sum_{r=1}^{20} (3r - 2)$ .
Level 3 · 2 marksTry it
4
(a) Evaluate $\displaystyle\sum_{r=1}^{15} (5r - 3)$ . (3 marks)
(b) Hence evaluate $\displaystyle\sum_{r=6}^{15} (5r - 3)$ . (2 marks)
Level 3 · 5 marksTry it
5
A sequence is defined by $u_{1} = 2$ and $u_{n+1} = \dfrac{1}{u_{n}}$ .
(a) Write down $u_{2}$ and $u_{3}$ , and describe the behaviour of the sequence. (2 marks)
(b) Write down $u_{50}$ . (1 mark)
(c) Find $\displaystyle\sum_{n=1}^{50} u_{n}$ . (2 marks)
Level 3 · 5 marksTry it

9 more questions on sigma notation and recurrence relations

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.