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

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.

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? 

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