Find the pattern in the sequence: 5, 9, 13, 17, 21, ...
Step 1 Find the differences
9 − 5 = 4
13 − 9 = 4
17 − 13 = 4
Common difference = 4
Step 2 Describe the pattern
Start with 5, add 4 each time
This is an arithmetic sequence
Step 3 Find the next terms
21 + 4 = 25
25 + 4 = 29
Next terms: 25, 29
This study notes covers Worked Example 1: Identifying Patterns within Sequences for GCSE Mathematics. Revise Sequences in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 4 of 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Sequences
What is the common difference of the arithmetic sequence below? 4, 11, 18, 25, 32, ...
Zara says: 'The sequence 4, 12, 36, 108 is an arithmetic sequence.' Explain why Zara is wrong. State what type of sequence it actually is.