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

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

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