Year 7 Sequences Practice

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📚 Part 1: Rules and Patterns

Worked example 1: In the sequence 4, 7, 10, 13, each term increases by 3. The term-to-term rule is add 3, so the next term is 16.

Worked example 2: The position-to-term rule 5n − 1 gives the sequence 4, 9, 14, 19, …

Worked example 3: In 3, 6, 12, 24, each term is multiplied by 2. This is a geometric sequence.

Support 1. Continue the sequence for three more terms: 8, 11, 14, 17, ______, ______, ______.

Support 2. Complete the sequence and state the term-to-term rule: −9, −5, ______, 3, ______.

Support 3. Is this sequence arithmetic or geometric? State the rule and find the next term: 2, 6, 18, 54, ______.

✏️ Part 2: Core Practice

Core 4. Find the term-to-term rule and write the next two terms: 25, 19, 13, 7, ______, ______.

Core 5. Find the nth-term rule for the sequence 7, 11, 15, 19, … Then use it to find the 20th term.

Core 6. Find the nth-term rule for the sequence −3, −8, −13, −18, …

Core 7. Complete the sequence and explain how you know: 4, ______, 16, ______, 28.

🚀 Part 3: Challenge and Conjectures

Challenge 8. Look at the sequence 2, 5, 10, 17, 26, … Find the next term. Describe the pattern in the differences and make a conjecture about the next difference.

Challenge 9. The sequence 20, 16, 12, 8, … has an nth-term rule. Find the rule and calculate the 15th term.

Challenge 10. Create an arithmetic sequence with a negative term and a positive term. Write its term-to-term rule and first five terms. Test your rule by finding the sixth term.