Year 4 Maths: Sequences

What is a Sequence?

A sequence is a list of numbers that follow a certain pattern. Each number in the sequence is called a term. Understanding sequences can help you see patterns in numbers and solve problems.

Examples of Sequences

1. Counting Numbers:
   • Sequence: 1, 2, 3, 4, 5, …
   • Pattern: We are adding 1 each time.
2. Even Numbers:
   • Sequence: 2, 4, 6, 8, 10, …
   • Pattern: We are adding 2 each time.
3. Odd Numbers:
   • Sequence: 1, 3, 5, 7, 9, …
   • Pattern: We are adding 2 each time.
4. Multiples of 3:
   • Sequence: 3, 6, 9, 12, 15, …
   • Pattern: We are adding 3 each time.

Key Rules for Sequences

1. Identify the Pattern: Look at how the numbers change. Are they increasing or decreasing? Are they adding, subtracting, multiplying, or dividing?
2. Use the First Few Terms: Start with the first few numbers to figure out the rule.
3. Continue the Sequence: Once you find the rule, you can find the next numbers in the sequence.

Tips and Tricks

• Write it Down: Sometimes, writing the sequence can help you see the pattern more clearly.
• Draw a Number Line: This can also help you visualise how the numbers are spaced out.
• Check Your Work: After finding the next numbers, double-check to make sure they follow the same pattern.

Questions on Sequences

Easy Level Questions

1. What are the first five terms in the sequence: 5, 10, 15, …?
2. What comes next in the sequence: 1, 2, 3, …?
3. What is the next number: 4, 8, 12, …?
4. Fill in the blank: 2, __, 6, 8.
5. What are the first three even numbers?
6. What comes next: 7, 14, 21, …?
7. What is the missing number in this sequence: 10, __, 30?
8. What are the first four terms of the sequence of odd numbers?
9. What comes after 20 in the sequence of counting numbers?
10. Write the next term: 3, 6, 9, …?

Medium Level Questions

1. What are the first five terms in the sequence: 10, 20, 30, …?
2. Fill in the blank: 1, 4, __, 16 (Hint: Square numbers).
3. What is the next number: 5, 10, 15, 20, …?
4. What comes next in this sequence: 2, 4, 8, 16, …?
5. What are the first three multiples of 4?
6. Complete the sequence: 3, 6, 9, 12, __?
7. What are the next two terms in this sequence: 1, 2, 4, 8, …?
8. What comes after 25 in the sequence of odd numbers?
9. Fill in the blank: 5, 10, __, 20.
10. What is the next term: 12, 10, 8, …?

Hard Level Questions

1. What is the 10th term in the sequence: 1, 4, 9, 16, …?
2. What are the first five terms of the sequence that multiplies by 2 each time, starting from 1?
3. Complete the sequence: 100, 90, 80, …?
4. What is the next number in the sequence: 3, 7, 11, …?
5. Find the next two terms: 2, 5, 10, 17, …?
6. What is the 5th term in the sequence: 5, 10, 15, …?
7. What comes after 18 in this sequence: 2, 6, 12, 20, …?
8. Fill in the blank: 25, 20, __, 10.
9. What is the next number in the sequence: 1, 1, 2, 3, 5, …?
10. What is the 7th term in the sequence: 10, 20, 30, …?

Answers and Explanations

Easy Level Answers

1. 20, 25, 30, 35, 40 (adding 5).
2. 4 (adding 1).
3. 16 (adding 4).
4. 4 (adding 2).
5. 0, 2, 4 (even numbers).
6. 28 (adding 7).
7. 20 (adding 10).
8. 1, 3, 5, 7 (odd numbers).
9. 21 (adding 1).
10. 12 (adding 3).

Medium Level Answers

1. 40, 50, 60, 70, 80 (adding 10).
2. 9 (squares: 1, 4, 9, 16).
3. 25 (adding 5).
4. 32 (doubling).
5. 4, 8, 12 (multiples of 4).
6. 15 (adding 3).
7. 16, 32 (doubling).
8. 27 (odd numbers).
9. 15 (adding 5).
10. 6 (subtracting 2).

Hard Level Answers

1. 100 (squares of 1 through 10).
2. 2, 4, 8, 16, 32 (doubling).
3. 70 (subtracting 10).
4. 15 (adding 4).
5. 26, 37 (adding odd numbers).
6. 50 (adding 5).
7. 30 (adding 12).
8. 15 (subtracting 5).
9. 8 (Fibonacci sequence).
10. 70 (adding 10).

By practicing with these questions, you’ll get better at spotting patterns and understanding sequences! Keep up the great work!