Number sequences worksheet for practicing pattern recognition and arithmetic skills.
Worksheet titled "Number Sequences or Patterns" with 15 numbered sequences of numbers, asking to write the next three numbers in each sequence.
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Step-by-step solution for: Number Sequence Worksheet worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Number Sequence Worksheet worksheet
Let's solve each sequence one by one and determine the next three numbers. We'll identify the pattern in each sequence and then extend it.
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1. 12, 23, 34, 45, ...
- Differences:
23 - 12 = 11
34 - 23 = 11
45 - 34 = 11
→ +11 each time
Next three:
45 + 11 = 56
56 + 11 = 67
67 + 11 = 78
✔ Answer: 56, 67, 78
---
2. 36, 33, 30, 27, ...
- Differences:
33 - 36 = -3
30 - 33 = -3
27 - 30 = -3
→ -3 each time
Next three:
27 - 3 = 24
24 - 3 = 21
21 - 3 = 18
✔ Answer: 24, 21, 18
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3. 3, 6, 12, 24, ...
- Pattern: Each term is multiplied by 2
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
Next three:
24 × 2 = 48
48 × 2 = 96
96 × 2 = 192
✔ Answer: 48, 96, 192
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4. 729, 243, 81, ...
- 729 ÷ 3 = 243
243 ÷ 3 = 81
→ Divided by 3 each time
Next three:
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
✔ Answer: 27, 9, 3
---
5. 1, 2, 4, 8, ...
- Each term ×2
1×2=2, 2×2=4, 4×2=8
Next three:
8×2 = 16
16×2 = 32
32×2 = 64
✔ Answer: 16, 32, 64
---
6. 1, 10, 100, 1000, ...
- Multiplying by 10 each time
1×10=10, 10×10=100, 100×10=1000
Next three:
1000×10 = 10,000
10,000×10 = 100,000
100,000×10 = 1,000,000
✔ Answer: 10,000, 100,000, 1,000,000
---
7. 100, 81, 64, 49, ...
- These are perfect squares:
100 = 10²
81 = 9²
64 = 8²
49 = 7²
→ Decreasing squares of integers
Next:
6² = 36
5² = 25
4² = 16
✔ Answer: 36, 25, 16
---
8. 30, 31, 34, 39, ...
- Differences:
31 - 30 = 1
34 - 31 = 3
39 - 34 = 5
→ Increasing odd numbers: +1, +3, +5 → next should be +7, +9, +11
Next:
39 + 7 = 46
46 + 9 = 55
55 + 11 = 66
✔ Answer: 46, 55, 66
---
9. 5, 6, 8, 11, ...
- Differences:
6 - 5 = 1
8 - 6 = 2
11 - 8 = 3
→ Increasing by +1 each time: +1, +2, +3 → next: +4, +5, +6
Next:
11 + 4 = 15
15 + 5 = 20
20 + 6 = 26
✔ Answer: 15, 20, 26
---
10. 1, 4, 9, 16, ...
- Perfect squares:
1² = 1
2² = 4
3² = 9
4² = 16
→ Next: 5² = 25, 6² = 36, 7² = 49
✔ Answer: 25, 36, 49
---
11. 30, 29, 27, 24, ...
- Differences:
29 - 30 = -1
27 - 29 = -2
24 - 27 = -3
→ Subtracting increasing integers: -1, -2, -3 → next: -4, -5, -6
Next:
24 - 4 = 20
20 - 5 = 15
15 - 6 = 9
✔ Answer: 20, 15, 9
---
12. 1, 3, 9, 27, ...
- Pattern: ×3 each time
1×3=3, 3×3=9, 9×3=27
Next:
27×3 = 81
81×3 = 243
243×3 = 729
✔ Answer: 81, 243, 729
---
13. 60, 52, 44, 36, ...
- Differences:
52 - 60 = -8
44 - 52 = -8
36 - 44 = -8
→ Subtract 8 each time
Next:
36 - 8 = 28
28 - 8 = 20
20 - 8 = 12
✔ Answer: 28, 20, 12
---
14. 64, 32, 16, 8, ...
- Divide by 2 each time:
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
Next:
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
✔ Answer: 4, 2, 1
---
15. 65, 55, 45, 35, ...
- Differences:
55 - 65 = -10
45 - 55 = -10
35 - 45 = -10
→ Subtract 10 each time
Next:
35 - 10 = 25
25 - 10 = 15
15 - 10 = 5
✔ Answer: 25, 15, 5
---
1. 56, 67, 78
2. 24, 21, 18
3. 48, 96, 192
4. 27, 9, 3
5. 16, 32, 64
6. 10,000, 100,000, 1,000,000
7. 36, 25, 16
8. 46, 55, 66
9. 15, 20, 26
10. 25, 36, 49
11. 20, 15, 9
12. 81, 243, 729
13. 28, 20, 12
14. 4, 2, 1
15. 25, 15, 5
Let me know if you'd like these explained in a table or printed format!
---
1. 12, 23, 34, 45, ...
- Differences:
23 - 12 = 11
34 - 23 = 11
45 - 34 = 11
→ +11 each time
Next three:
45 + 11 = 56
56 + 11 = 67
67 + 11 = 78
✔ Answer: 56, 67, 78
---
2. 36, 33, 30, 27, ...
- Differences:
33 - 36 = -3
30 - 33 = -3
27 - 30 = -3
→ -3 each time
Next three:
27 - 3 = 24
24 - 3 = 21
21 - 3 = 18
✔ Answer: 24, 21, 18
---
3. 3, 6, 12, 24, ...
- Pattern: Each term is multiplied by 2
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
Next three:
24 × 2 = 48
48 × 2 = 96
96 × 2 = 192
✔ Answer: 48, 96, 192
---
4. 729, 243, 81, ...
- 729 ÷ 3 = 243
243 ÷ 3 = 81
→ Divided by 3 each time
Next three:
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
✔ Answer: 27, 9, 3
---
5. 1, 2, 4, 8, ...
- Each term ×2
1×2=2, 2×2=4, 4×2=8
Next three:
8×2 = 16
16×2 = 32
32×2 = 64
✔ Answer: 16, 32, 64
---
6. 1, 10, 100, 1000, ...
- Multiplying by 10 each time
1×10=10, 10×10=100, 100×10=1000
Next three:
1000×10 = 10,000
10,000×10 = 100,000
100,000×10 = 1,000,000
✔ Answer: 10,000, 100,000, 1,000,000
---
7. 100, 81, 64, 49, ...
- These are perfect squares:
100 = 10²
81 = 9²
64 = 8²
49 = 7²
→ Decreasing squares of integers
Next:
6² = 36
5² = 25
4² = 16
✔ Answer: 36, 25, 16
---
8. 30, 31, 34, 39, ...
- Differences:
31 - 30 = 1
34 - 31 = 3
39 - 34 = 5
→ Increasing odd numbers: +1, +3, +5 → next should be +7, +9, +11
Next:
39 + 7 = 46
46 + 9 = 55
55 + 11 = 66
✔ Answer: 46, 55, 66
---
9. 5, 6, 8, 11, ...
- Differences:
6 - 5 = 1
8 - 6 = 2
11 - 8 = 3
→ Increasing by +1 each time: +1, +2, +3 → next: +4, +5, +6
Next:
11 + 4 = 15
15 + 5 = 20
20 + 6 = 26
✔ Answer: 15, 20, 26
---
10. 1, 4, 9, 16, ...
- Perfect squares:
1² = 1
2² = 4
3² = 9
4² = 16
→ Next: 5² = 25, 6² = 36, 7² = 49
✔ Answer: 25, 36, 49
---
11. 30, 29, 27, 24, ...
- Differences:
29 - 30 = -1
27 - 29 = -2
24 - 27 = -3
→ Subtracting increasing integers: -1, -2, -3 → next: -4, -5, -6
Next:
24 - 4 = 20
20 - 5 = 15
15 - 6 = 9
✔ Answer: 20, 15, 9
---
12. 1, 3, 9, 27, ...
- Pattern: ×3 each time
1×3=3, 3×3=9, 9×3=27
Next:
27×3 = 81
81×3 = 243
243×3 = 729
✔ Answer: 81, 243, 729
---
13. 60, 52, 44, 36, ...
- Differences:
52 - 60 = -8
44 - 52 = -8
36 - 44 = -8
→ Subtract 8 each time
Next:
36 - 8 = 28
28 - 8 = 20
20 - 8 = 12
✔ Answer: 28, 20, 12
---
14. 64, 32, 16, 8, ...
- Divide by 2 each time:
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
Next:
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
✔ Answer: 4, 2, 1
---
15. 65, 55, 45, 35, ...
- Differences:
55 - 65 = -10
45 - 55 = -10
35 - 45 = -10
→ Subtract 10 each time
Next:
35 - 10 = 25
25 - 10 = 15
15 - 10 = 5
✔ Answer: 25, 15, 5
---
✔ Final Answers:
1. 56, 67, 78
2. 24, 21, 18
3. 48, 96, 192
4. 27, 9, 3
5. 16, 32, 64
6. 10,000, 100,000, 1,000,000
7. 36, 25, 16
8. 46, 55, 66
9. 15, 20, 26
10. 25, 36, 49
11. 20, 15, 9
12. 81, 243, 729
13. 28, 20, 12
14. 4, 2, 1
15. 25, 15, 5
Let me know if you'd like these explained in a table or printed format!
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet year 6.
