The nth term of a sequence is the position of a term in a sequence where n stands for the term number.

A term-to-term rule describes how to calculate the next term in the sequence from the previous term.

A Fibonacci sequence is a sequence where each term is the sum of the two previous terms.

Sequence notation

Maths

Checking and securing understanding of special number sequences

Fibonacci and alternating sequences

Checking and securing rules for generating arithmetic sequences

Identifying values in an arithmetic sequence

Reasoning about values in an arithmetic sequence

Conditions in arithmetic sequences

Arithmetic sequences and their graphs

Introducing quadratic sequences

Quadratic sequences

Checking and securing understanding of geometric sequences

Advanced problem solving with further sequences

In the prior unit, pupils considered other types of graphs. In this unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In this unit, pupils consider different types of sequences such as Fibonacci and oscillating sequences. They then consolidate their knowledge of different types of sequences by solving contextual problems.

Further sequences

Which of these would be the correct notation to refer to the third term in a sequence?

Which of these could be correct notation for the linear sequence 5, 9, 13, 17, 21, ... ?

A linear sequence has $$n^\text{th}$$ term rule $$5n +2$$ which of these could describe the same sequence? 

A sequence has rule $$u_{n+2} = u_{n} + u_{n+1} , u_1 = 6, u_2 = 2 $$. What is the $$5^\text{th}$$ term?

A sequence has form $$u_{n+1}= ku_n -3 , u_1 = 2$$ If $$u_3 = 6$$ then $$k= -\frac{3}{2}$$ or $$k=$${{}}

Which of these are the first 4 terms in the sequence with $$n^\text{th}$$ term rule $$4n+2$$?

What is the correct $$n^\text{th}$$ term rule for the linear sequence which starts 2, 7, 12, 17, ...?

Start on 3, add 2 to the previous term to get the next term.

Start on 3, double then subtract 1 to get the next term.

Start on 3, add 3 to the previous term to get the next term.

Start on 3, double the previous term to get the next term.

Start on 3, subtract 1 then multiply by 3 to get the next term.

Match the first 4 terms of these sequences with possible term-to-term rules.

What term number is 51 in the linear sequence which starts: 3, 9, 15, 21, ...?

A Fibonacci sequence starts 7, 11, 18, ... what is the fourth term?

A Fibonacci sequence has first term 4 and fourth term 14. What is the second term? 

Sequence notation

Lesson outcome