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.
Worked Example 1: Identifying Patterns
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
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.