Grade 4 Number Sequences Worksheets|www.grade1to6.com - Free Printable
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Step-by-step solution for: Grade 4 Number Sequences Worksheets|www.grade1to6.com
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Show Answer Key & Explanations
Step-by-step solution for: Grade 4 Number Sequences Worksheets|www.grade1to6.com
Let’s solve each sequence step by step, identifying the pattern and filling in the missing numbers.
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1. 14, 20, 26, 32, __, __
Look at the difference between terms:
- 20 - 14 = 6
- 26 - 20 = 6
- 32 - 26 = 6
✔ Pattern: Add 6 each time
Next two numbers:
- 32 + 6 = 38
- 38 + 6 = 44
Answer: 38, 44
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2. 47, 54, 61, 68, __, __
Differences:
- 54 - 47 = 7
- 61 - 54 = 7
- 68 - 61 = 7
✔ Pattern: Add 7 each time
Next two:
- 68 + 7 = 75
- 75 + 7 = 82
Answer: 75, 82
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3. 9, 17, __, 33, __, 49
Differences:
- 17 - 9 = 8
- Let’s assume pattern continues → next should be 17 + 8 = 25
- Then 25 + 8 = 33 ✔ matches
- Then 33 + 8 = 41
- Then 41 + 8 = 49 ✔ matches
✔ Pattern: Add 8 each time
Missing numbers: 25, 41
Answer: 25, 41
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4. 27, 34, __, __, __
Differences:
- 34 - 27 = 7
Assume add 7 each time:
- 34 + 7 = 41
- 41 + 7 = 48
- 48 + 7 = 55
✔ Pattern: Add 7
Answer: 41, 48, 55
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5. 67, 58, 49, __, 31, __
Differences:
- 58 - 67 = -9
- 49 - 58 = -9
✔ Pattern: Subtract 9 each time
Next:
- 49 - 9 = 40
- 31 - 9 = 22 (check: 40 - 9 = 31 ✔)
So missing numbers: 40, 22
Answer: 40, 22
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6. 99, 92, __, 78, __, 64
Differences:
- 92 - 99 = -7
Assume subtract 7:
- 92 - 7 = 85
- 85 - 7 = 78 ✔
- 78 - 7 = 71
- 71 - 7 = 64 ✔
Missing numbers: 85, 71
Answer: 85, 71
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7. __, 42, 36, 30, __, 18
Differences:
- 36 - 42 = -6
- 30 - 36 = -6
Pattern: Subtract 6
Before 42: 42 + 6 = 48
After 30: 30 - 6 = 24
Check: 24 - 6 = 18 ✔
Missing numbers: 48, 24
Answer: 48, 24
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8. __, __, 78, 70, 62, 54
Differences:
- 70 - 78 = -8
- 62 - 70 = -8
- 54 - 62 = -8
Pattern: Subtract 8
Before 78:
- 78 + 8 = 86
- 86 + 8 = 94
Missing numbers: 94, 86
Answer: 94, 86
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9. Take a 9 x 9 square. Starting at 1 count on in sevens. Circle or colour the numbers you land on.
We start at 1, then keep adding 7:
Sequence:
- 1
- 1 + 7 = 8
- 8 + 7 = 15
- 15 + 7 = 22
- 22 + 7 = 29
- 29 + 7 = 36
- 36 + 7 = 43
- 43 + 7 = 50
- 50 + 7 = 57
- 57 + 7 = 64
- 64 + 7 = 71
- 71 + 7 = 78
- 78 + 7 = 85
- 85 + 7 = 92 → but our grid only goes to 81, so we stop before that.
✔ Numbers to circle:
1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85
(But since the grid ends at 81, you would circle up to 78 — 85 is outside the grid.)
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10. What do you notice? If you went on, would 100 be in your sequence? How do you know?
✔ What you notice:
- All numbers are 1 more than a multiple of 7.
- In other words, they leave a remainder of 1 when divided by 7.
- 1 ÷ 7 = 0 R1
- 8 ÷ 7 = 1 R1
- 15 ÷ 7 = 2 R1
- etc.
This is an arithmetic sequence starting at 1, with common difference 7.
✔ Would 100 be in the sequence?
Check: Does 100 leave a remainder of 1 when divided by 7?
100 ÷ 7 = 14 * 7 = 98 → 100 - 98 = 2
So 100 ÷ 7 = 14 remainder 2 → not 1.
Therefore, 100 is NOT in the sequence.
✔ How do you know?
Because every number in the sequence follows the formula:
n = 7k + 1 for integer k ≥ 0.
Set 7k + 1 = 100 → 7k = 99 → k = 99/7 ≈ 14.14 → not an integer → so 100 is not in the sequence.
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1. 38, 44
2. 75, 82
3. 25, 41
4. 41, 48, 55
5. 40, 22
6. 85, 71
7. 48, 24
8. 94, 86
9. Circle: 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78 (and 85 if grid allowed)
10. All numbers are 1 more than multiples of 7. 100 is NOT in the sequence because 100 mod 7 = 2, not 1.
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Let me know if you’d like this formatted as a worksheet answer key!
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1. 14, 20, 26, 32, __, __
Look at the difference between terms:
- 20 - 14 = 6
- 26 - 20 = 6
- 32 - 26 = 6
✔ Pattern: Add 6 each time
Next two numbers:
- 32 + 6 = 38
- 38 + 6 = 44
Answer: 38, 44
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2. 47, 54, 61, 68, __, __
Differences:
- 54 - 47 = 7
- 61 - 54 = 7
- 68 - 61 = 7
✔ Pattern: Add 7 each time
Next two:
- 68 + 7 = 75
- 75 + 7 = 82
Answer: 75, 82
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3. 9, 17, __, 33, __, 49
Differences:
- 17 - 9 = 8
- Let’s assume pattern continues → next should be 17 + 8 = 25
- Then 25 + 8 = 33 ✔ matches
- Then 33 + 8 = 41
- Then 41 + 8 = 49 ✔ matches
✔ Pattern: Add 8 each time
Missing numbers: 25, 41
Answer: 25, 41
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4. 27, 34, __, __, __
Differences:
- 34 - 27 = 7
Assume add 7 each time:
- 34 + 7 = 41
- 41 + 7 = 48
- 48 + 7 = 55
✔ Pattern: Add 7
Answer: 41, 48, 55
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5. 67, 58, 49, __, 31, __
Differences:
- 58 - 67 = -9
- 49 - 58 = -9
✔ Pattern: Subtract 9 each time
Next:
- 49 - 9 = 40
- 31 - 9 = 22 (check: 40 - 9 = 31 ✔)
So missing numbers: 40, 22
Answer: 40, 22
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6. 99, 92, __, 78, __, 64
Differences:
- 92 - 99 = -7
Assume subtract 7:
- 92 - 7 = 85
- 85 - 7 = 78 ✔
- 78 - 7 = 71
- 71 - 7 = 64 ✔
Missing numbers: 85, 71
Answer: 85, 71
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7. __, 42, 36, 30, __, 18
Differences:
- 36 - 42 = -6
- 30 - 36 = -6
Pattern: Subtract 6
Before 42: 42 + 6 = 48
After 30: 30 - 6 = 24
Check: 24 - 6 = 18 ✔
Missing numbers: 48, 24
Answer: 48, 24
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8. __, __, 78, 70, 62, 54
Differences:
- 70 - 78 = -8
- 62 - 70 = -8
- 54 - 62 = -8
Pattern: Subtract 8
Before 78:
- 78 + 8 = 86
- 86 + 8 = 94
Missing numbers: 94, 86
Answer: 94, 86
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9. Take a 9 x 9 square. Starting at 1 count on in sevens. Circle or colour the numbers you land on.
We start at 1, then keep adding 7:
Sequence:
- 1
- 1 + 7 = 8
- 8 + 7 = 15
- 15 + 7 = 22
- 22 + 7 = 29
- 29 + 7 = 36
- 36 + 7 = 43
- 43 + 7 = 50
- 50 + 7 = 57
- 57 + 7 = 64
- 64 + 7 = 71
- 71 + 7 = 78
- 78 + 7 = 85
- 85 + 7 = 92 → but our grid only goes to 81, so we stop before that.
✔ Numbers to circle:
1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85
(But since the grid ends at 81, you would circle up to 78 — 85 is outside the grid.)
---
10. What do you notice? If you went on, would 100 be in your sequence? How do you know?
✔ What you notice:
- All numbers are 1 more than a multiple of 7.
- In other words, they leave a remainder of 1 when divided by 7.
- 1 ÷ 7 = 0 R1
- 8 ÷ 7 = 1 R1
- 15 ÷ 7 = 2 R1
- etc.
This is an arithmetic sequence starting at 1, with common difference 7.
✔ Would 100 be in the sequence?
Check: Does 100 leave a remainder of 1 when divided by 7?
100 ÷ 7 = 14 * 7 = 98 → 100 - 98 = 2
So 100 ÷ 7 = 14 remainder 2 → not 1.
Therefore, 100 is NOT in the sequence.
✔ How do you know?
Because every number in the sequence follows the formula:
n = 7k + 1 for integer k ≥ 0.
Set 7k + 1 = 100 → 7k = 99 → k = 99/7 ≈ 14.14 → not an integer → so 100 is not in the sequence.
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✔ Final Answers:
1. 38, 44
2. 75, 82
3. 25, 41
4. 41, 48, 55
5. 40, 22
6. 85, 71
7. 48, 24
8. 94, 86
9. Circle: 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78 (and 85 if grid allowed)
10. All numbers are 1 more than multiples of 7. 100 is NOT in the sequence because 100 mod 7 = 2, not 1.
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Let me know if you’d like this formatted as a worksheet answer key!
Parent Tip: Review the logic above to help your child master the concept of number sequencing worksheets.
