The Fibonacci Sequence

Here are a selection of sequences maths worksheets with answers, starting with the term to term rule, and more advanced concepts like geometric sequences at worksheet number 7.

Generating Sequences

The graphic below shows expressions written as n which generate linear sequences.  Finding the nth term for 3n + 2, n(1) = 5, n(2) = 8, n(3) = 11 and n(4) = 14. Finding the nth term for 4n - 1, n(1) = 3, n(2) = 7, n(3) = 11 and n(4) = 15.  Finding the nth term for 7 - 2n, n(1) = 5, n(2) = 3, n(3) = 1 and n(4) = - 1. Linear sequences can be ascending or descending. Generating sequences involves substitution.

Sequences - Key Words

Geometric sequences was introduced in the UK curriculum with the introduction of the 9-1 grading system. It was previously a topic exclusive to A-Level mathematics. Suggested after topics include: quadratic graphs and functions.

Linear Sequences vs Quadratic Sequences

The diagrams below show two linear sequences and one quadratic sequence. The first linear sequence has a common difference of positive 4. The second linear sequence has a common difference of positive 5. See quadratic sequences to learn how to interpret quadratic sequences.

The image below shows the linear sequence 0, 4, 8, 12, 16. The nth term is 4n - 4.

The image below shows the linear sequence 1, 6, 11, 16, 21. The nth term is 5n - 4.

The image below shows the quadratic sequence 9, 12, 17, 24 , 33. The nth term is n² + 8.