Math worksheet focusing on identifying and continuing number patterns and sequences.
Worksheet titled "Sequence and Number Patterns" with 21 numbered sequences requiring the next two terms to be filled in.
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Step-by-step solution for: Sequence and Number Pattern worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Sequence and Number Pattern worksheet
To solve the problem, we need to identify the pattern in each sequence and determine the next two terms. Let's go through each sequence step by step.
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- The sequence is increasing by 1 each time.
- Next terms: \(9 + 1 = 10\), \(10 + 1 = 11\).
- Answer: \(10, 11\).
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- The sequence is decreasing by 8 each time.
- Next terms: \(64 - 8 = 56\), \(56 - 8 = 48\).
- Answer: \(56, 48\).
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- This is the Fibonacci sequence, where each term is the sum of the previous two terms.
- Next terms: \(2 + 3 = 5\), \(3 + 5 = 8\).
- Answer: \(5, 8\).
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- The sequence is decreasing by 4 each time.
- Next terms: \(12 - 4 = 8\), \(8 - 4 = 4\).
- Answer: \(8, 4\).
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- The sequence is increasing by 8 each time.
- Next terms: \(34 + 8 = 42\), \(42 + 8 = 50\).
- Answer: \(42, 50\).
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- These are perfect squares: \(2^2, 3^2, 4^2, 5^2\).
- Next terms: \(6^2 = 36\), \(7^2 = 49\).
- Answer: \(36, 49\).
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- The sequence increases by 20, then 20 again.
- Next terms: \(48 + 20 = 68\), \(68 + 20 = 88\).
- Answer: \(68, 88\).
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- Each term is multiplied by 2.
- Next terms: \(8 \times 2 = 16\), \(16 \times 2 = 32\).
- Answer: \(16, 32\).
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- This is a modified Fibonacci sequence where each term is the sum of the previous two terms.
- Next terms: \(8 + 13 = 21\), \(13 + 21 = 34\).
- Answer: \(21, 34\).
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- These are prime numbers in ascending order.
- Next terms: The next two prime numbers after 23 are 29 and 31.
- Answer: \(29, 31\).
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- These are odd numbers in ascending order.
- Next terms: \(7 + 2 = 9\), \(9 + 2 = 11\).
- Answer: \(9, 11\).
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- The sequence increases by 12 each time.
- Next terms: \(48 + 12 = 60\), \(60 + 12 = 72\).
- Answer: \(60, 72\).
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- The sequence decreases by 1 each time.
- Next terms: \(-10 - 1 = -11\), \(-11 - 1 = -12\).
- Answer: \(-11, -12\).
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- The sequence decreases by 100 each time.
- Next terms: \(1300 - 100 = 1200\), \(1200 - 100 = 1100\).
- Answer: \(1200, 1100\).
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- The sequence decreases by 4 each time.
- Next terms: \(65 - 4 = 61\), \(61 - 4 = 57\).
- Answer: \(61, 57\).
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- The sequence increases by 0.2, then 0.2 again.
- Next terms: \(0.8 + 0.2 = 1.0\), \(1.0 + 0.2 = 1.2\).
- Answer: \(1.0, 1.2\).
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- The sequence increases by 1 each time.
- Next terms: \(-1 + 1 = 0\), \(0 + 1 = 1\).
- Answer: \(0, 1\).
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- The sequence increases by 9 each time.
- Next terms: \(81 + 9 = 90\), \(90 + 9 = 99\).
- Answer: \(90, 99\).
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- These are cubes: \(1^3, 2^3, 3^3\).
- Next terms: \(4^3 = 64\), \(5^3 = 125\).
- Answer: \(64, 125\).
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- These are perfect squares: \(12^2, 13^2, 14^2\).
- Next terms: \(15^2 = 225\), \(16^2 = 256\).
- Answer: \(225, 256\).
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- The sequence increases by 1.5 each time.
- Next terms: \(5.3 + 1.5 = 6.8\), \(6.8 + 1.5 = 8.3\) (already given).
- Answer: \(6.8, 8.3\).
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1. \(10, 11\)
2. \(56, 48\)
3. \(5, 8\)
4. \(8, 4\)
5. \(42, 50\)
6. \(36, 49\)
7. \(68, 88\)
8. \(16, 32\)
9. \(21, 34\)
10. \(29, 31\)
11. \(9, 11\)
12. \(60, 72\)
13. \(-11, -12\)
14. \(1200, 1100\)
15. \(61, 57\)
16. \(1.0, 1.2\)
17. \(0, 1\)
18. \(90, 99\)
19. \(64, 125\)
20. \(225, 256\)
21. \(6.8, 8.3\)
\(\boxed{10, 11; 56, 48; 5, 8; 8, 4; 42, 50; 36, 49; 68, 88; 16, 32; 21, 34; 29, 31; 9, 11; 60, 72; -11, -12; 1200, 1100; 61, 57; 1.0, 1.2; 0, 1; 90, 99; 64, 125; 225, 256; 6.8, 8.3}\)
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Sequence 1: \(7, 8, 9, \_, \_\)
- The sequence is increasing by 1 each time.
- Next terms: \(9 + 1 = 10\), \(10 + 1 = 11\).
- Answer: \(10, 11\).
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Sequence 2: \(80, 72, 64, \_, \_\)
- The sequence is decreasing by 8 each time.
- Next terms: \(64 - 8 = 56\), \(56 - 8 = 48\).
- Answer: \(56, 48\).
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Sequence 3: \(1, 1, 2, 3, \_, \_\)
- This is the Fibonacci sequence, where each term is the sum of the previous two terms.
- Next terms: \(2 + 3 = 5\), \(3 + 5 = 8\).
- Answer: \(5, 8\).
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Sequence 4: \(20, 16, 12, \_, \_\)
- The sequence is decreasing by 4 each time.
- Next terms: \(12 - 4 = 8\), \(8 - 4 = 4\).
- Answer: \(8, 4\).
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Sequence 5: \(18, 26, 34, \_, \_\)
- The sequence is increasing by 8 each time.
- Next terms: \(34 + 8 = 42\), \(42 + 8 = 50\).
- Answer: \(42, 50\).
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Sequence 6: \(4, 9, 16, 25, \_, \_\)
- These are perfect squares: \(2^2, 3^2, 4^2, 5^2\).
- Next terms: \(6^2 = 36\), \(7^2 = 49\).
- Answer: \(36, 49\).
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Sequence 7: \(8, 28, 48, \_, \_\)
- The sequence increases by 20, then 20 again.
- Next terms: \(48 + 20 = 68\), \(68 + 20 = 88\).
- Answer: \(68, 88\).
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Sequence 8: \(1, 2, 4, 8, \_, \_\)
- Each term is multiplied by 2.
- Next terms: \(8 \times 2 = 16\), \(16 \times 2 = 32\).
- Answer: \(16, 32\).
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Sequence 9: \(3, 5, 8, 13, \_, \_\)
- This is a modified Fibonacci sequence where each term is the sum of the previous two terms.
- Next terms: \(8 + 13 = 21\), \(13 + 21 = 34\).
- Answer: \(21, 34\).
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Sequence 10: \(17, 19, 23, \_, \_\)
- These are prime numbers in ascending order.
- Next terms: The next two prime numbers after 23 are 29 and 31.
- Answer: \(29, 31\).
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Sequence 11: \(3, 5, 7, \_, \_\)
- These are odd numbers in ascending order.
- Next terms: \(7 + 2 = 9\), \(9 + 2 = 11\).
- Answer: \(9, 11\).
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Sequence 12: \(24, 36, 48, \_, \_\)
- The sequence increases by 12 each time.
- Next terms: \(48 + 12 = 60\), \(60 + 12 = 72\).
- Answer: \(60, 72\).
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Sequence 13: \(-8, -9, -10, \_, \_\)
- The sequence decreases by 1 each time.
- Next terms: \(-10 - 1 = -11\), \(-11 - 1 = -12\).
- Answer: \(-11, -12\).
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Sequence 14: \(1500, 1400, 1300, \_, \_\)
- The sequence decreases by 100 each time.
- Next terms: \(1300 - 100 = 1200\), \(1200 - 100 = 1100\).
- Answer: \(1200, 1100\).
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Sequence 15: \(77, 73, 69, 65, \_, \_\)
- The sequence decreases by 4 each time.
- Next terms: \(65 - 4 = 61\), \(61 - 4 = 57\).
- Answer: \(61, 57\).
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Sequence 16: \(0.2, 0.6, 0.8, \_, \_\)
- The sequence increases by 0.2, then 0.2 again.
- Next terms: \(0.8 + 0.2 = 1.0\), \(1.0 + 0.2 = 1.2\).
- Answer: \(1.0, 1.2\).
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Sequence 17: \(-3, -2, -1, \_, \_\)
- The sequence increases by 1 each time.
- Next terms: \(-1 + 1 = 0\), \(0 + 1 = 1\).
- Answer: \(0, 1\).
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Sequence 18: \(63, 72, 81, \_, \_\)
- The sequence increases by 9 each time.
- Next terms: \(81 + 9 = 90\), \(90 + 9 = 99\).
- Answer: \(90, 99\).
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Sequence 19: \(1, 8, 27, \_, \_\)
- These are cubes: \(1^3, 2^3, 3^3\).
- Next terms: \(4^3 = 64\), \(5^3 = 125\).
- Answer: \(64, 125\).
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Sequence 20: \(144, 169, 196, \_, \_\)
- These are perfect squares: \(12^2, 13^2, 14^2\).
- Next terms: \(15^2 = 225\), \(16^2 = 256\).
- Answer: \(225, 256\).
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Sequence 21: \(2.3, 3.8, 5.3, \_, \_, 8.3, 9.8, 11.3\)
- The sequence increases by 1.5 each time.
- Next terms: \(5.3 + 1.5 = 6.8\), \(6.8 + 1.5 = 8.3\) (already given).
- Answer: \(6.8, 8.3\).
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Final Answers:
1. \(10, 11\)
2. \(56, 48\)
3. \(5, 8\)
4. \(8, 4\)
5. \(42, 50\)
6. \(36, 49\)
7. \(68, 88\)
8. \(16, 32\)
9. \(21, 34\)
10. \(29, 31\)
11. \(9, 11\)
12. \(60, 72\)
13. \(-11, -12\)
14. \(1200, 1100\)
15. \(61, 57\)
16. \(1.0, 1.2\)
17. \(0, 1\)
18. \(90, 99\)
19. \(64, 125\)
20. \(225, 256\)
21. \(6.8, 8.3\)
\(\boxed{10, 11; 56, 48; 5, 8; 8, 4; 42, 50; 36, 49; 68, 88; 16, 32; 21, 34; 29, 31; 9, 11; 60, 72; -11, -12; 1200, 1100; 61, 57; 1.0, 1.2; 0, 1; 90, 99; 64, 125; 225, 256; 6.8, 8.3}\)
Parent Tip: Review the logic above to help your child master the concept of pattern sequence worksheet grade.
