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

An alternating sequence is a sequence where consecutive terms change sign.

Fibonacci and alternating sequences

Maths

Checking and securing understanding of special number 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

Checking and securing understanding of geometric sequences

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

A sequence where consecutive terms change sign is called __________

Match the types of sequence to an example of a possible first 5 terms. 

Here are the first 7 terms in the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, ... What is the next term?

Here is a Fibonacci sequence. What is the missing first term?: {{}}, 6, 11, 17, 28, ... 

Here is a Fibonacci sequence. What is the missing term?:  4, ___, 2, 0, 2, ... 

If the first term in a Fibonacci sequence is 12 and the fourth term is 28, what is the second term?

Which of these could be the first 5 terms in an arithmetic (linear) sequence?

Which of these could be the first 5 terms in a geometric sequence?

State the $$10^\text {th}$$ term in the sequence with $$n^\text{th}$$ term rule $$3n +1$$

Which sequence could be 'two more than the square numbers'?

If a geometric sequence starts 4, 8, 16, 32, ... what is the common ratio (multiplier)?

If a geometric sequence starts 8, -12, 18, -27, ... what is the common ratio (multiplier)?

Fibonacci and alternating sequences

Lesson outcome