An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

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

Checking and securing rules for generating arithmetic sequences

Maths

Checking and securing understanding of special number sequences

Fibonacci and alternating 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

Sequence notation

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

it does not have a common multiplicative difference between successive terms

it does not have a common additive difference between successive terms

$$4,5,7,8,10,11,13, ...$$ is not an arithmetic sequence because __________.

What is the next term in this arithmetic sequence? $$7, 18, 29, ...$$ {{}}

What is the next term in this arithmetic sequence? $$41, 189, ...$$ {{}}

$${3\over7}, {6\over7}, {9\over7}, {12\over7}, ...$$

$${7\over3}, {7\over6}, {7\over9}, {7\over12}, ...$$

What is the $$n^\text{th}$$ term rule of this arithmetic sequence? $$9, 16, 23, 30, ...$$

What is the $$n^\text{th}$$ term rule of this arithmetic sequence? $$1, 0.4, -0.2, -0.8, ...$$

In the sequence $$3, 7, 11, 15, 19, ...$$ 'add four' is the __________.

What is the next term in this sequence? $$17, 23, 29, 35,$$ {{}}

What is the next term in this sequence? $$18, 11, 4, -3, ...$$

What is the common additive difference in this sequence? $$4, -1, -6, -11, ...$$

What is the next term in this sequence? $$1, 3, 6, 10, 15, ...$$ {{}}

What is the $$10^\text{th}$$ term in this sequence? $$-11, -2, 7, 16, 25, ...$$ {{}}

Starter Quiz

In the sequence $$3, 7, 11, 15, 19, ...$$ 'add four' is the __________.