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Year 7 Sequences Worksheet

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Year 7 Sequences Worksheet worksheet preview

Year 7 Sequences Worksheet

Mathematical sequences illustration

📚 Understanding Sequences

Key Tips:

• A sequence is a list of numbers that follow a pattern

• Look for what you add or subtract to get from one term to the next

• The difference between consecutive terms is called the "common difference"

1. Which of these is an arithmetic sequence (where you add the same number each time)?

2, 4, 8, 16, 32...

3, 7, 11, 15, 19...

1, 4, 9, 16, 25...

5, 10, 8, 13, 11...

2. In the sequence 4, 9, 14, 19, 24..., what number do you add each time?
3. Find the next two terms in each sequence:

a) 6, 11, 16, 21, _____, _____

b) 50, 45, 40, 35, _____, _____

c) 1, 8, 15, 22, _____, _____

4. Circle the sequences that are decreasing (getting smaller):

100, 90, 80, 70...

2, 5, 8, 11...

30, 25, 20, 15...

1, 3, 5, 7...

✏️ Finding Terms and Patterns

5. For the sequence 7, 12, 17, 22, 27..., find:

a) The 6th term: _____

b) The 10th term: _____

6. A sequence starts with 3 and increases by 4 each time. Write the first 6 terms:

_____, _____, _____, _____, _____, _____

7. The nth term of a sequence is given by n + 5. Find:

a) 1st term: _____

b) 5th term: _____

c) 20th term: _____

8. Match each sequence to its pattern:
5, 10, 15, 20...
8, 6, 4, 2...
1, 4, 7, 10...
Add 3
Add 5
Subtract 2

🎯 Problem Solving with Sequences

9. Sarah saves money each week. She starts with £5 and saves £3 more each week. How much will she have after 8 weeks?
10. A cinema has 20 seats in the first row, 23 in the second row, 26 in the third row, and so on. How many seats are in the 7th row?
11. Create your own arithmetic sequence that:

a) Starts with 12 and increases by 6: _____, _____, _____, _____, _____

b) Starts with 50 and decreases by 7: _____, _____, _____, _____, _____

12. Challenge: If the 5th term of a sequence is 23 and the common difference is 4, what is the first term?

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