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The pattern formed in this flower relates to a number sequence called the Fibonacci Sequence.

Sequences (F)

Learn GCSE sequences: spot term-to-term rules, find the nth term for arithmetic sequences, and use patterns to predict values, check membership, and solve exam-style problems.

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Fascinating Fact:

On a savings plan, the nth term of an arithmetic sequence equals a + (n − 1)d. For first term a = 5 and d = 2, nth term equals 5 + (n − 1)×2.

In GCSE Maths, sequences are ordered lists that follow a pattern. You will use term-to-term rules and find an nth-term formula to generate values, test membership, and solve problems.

Key Terms

Sequence: An ordered list of numbers that follow a rule (e.g., 3, 7, 11, 15, ...).
Term-to-term rule: How to get from one term to the next, such as “add 4.”
nth term: A formula that gives the value of the nth term directly, e.g., u_n = 3n − 2.

Frequently Asked Questions (Click to see answers)

How do I find the nth term of an arithmetic sequence?

Find the common difference d. Use u_n = a + (n − 1)d, where a is the first term. Example: 5, 9, 13,... has d = 4 so u_n = 5 + (n − 1)4 = 4n + 1.

What is the difference between a term-to-term rule and an nth-term formula?

A term-to-term rule tells you how to get the next term (e.g., “+3”). An nth-term formula gives any term directly from n (e.g., u_n = 3n + 2).

How do I check if a number is in a sequence?

Set the nth-term formula equal to the number and solve for n. If n is a positive whole number, the number is in the sequence.