Math worksheet titled Mastery Check: Patterns featuring seven number sequence problems and a rule-based pattern exercise.

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Part 1: Continue each pattern and write whether it is arithmetic, geometric, or neither

We will analyze each sequence, find the pattern, continue it, and classify it.

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#### 1. 24, 34, 33, 43, 42, ____, ____, ____, ____, ____

Let’s look at the pattern:

- 24 → 34 (+10)
- 34 → 33 (−1)
- 33 → 43 (+10)
- 43 → 42 (−1)

So the pattern alternates: +10, −1, +10, −1, ...

Continue:
- 42 → 52 (+10)
- 52 → 51 (−1)
- 51 → 61 (+10)
- 61 → 60 (−1)
- 60 → 70 (+10)

Sequence: 24, 34, 33, 43, 42, 52, 51, 61, 60, 70

Type: Neither (alternating operations, not constant difference or ratio)

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#### 2. 1, 1, 2, 3, 5, ____, ____, ____, ____, ____

This is the Fibonacci sequence: each term is the sum of the two previous terms.

- 1, 1, 2, 3, 5
- 5 + 3 = 8
- 8 + 5 = 13
- 13 + 8 = 21
- 21 + 13 = 34
- 34 + 21 = 55

Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Type: Neither (each term is sum of two prior terms – recursive, not arithmetic or geometric)

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#### 3. 76, 69, 62, 55, 48, ____, ____, ____, ____, ____

Check differences:
- 76 → 69 (−7)
- 69 → 62 (−7)
- 62 → 55 (−7)
- 55 → 48 (−7)

Constant difference: −7

So this is an arithmetic sequence.

Continue:
- 48 − 7 = 41
- 41 − 7 = 34
- 34 − 7 = 27
- 27 − 7 = 20
- 20 − 7 = 13

Sequence: 76, 69, 62, 55, 48, 41, 34, 27, 20, 13

Type: Arithmetic

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#### 4. 7, 21, 63, 189, 567, ____, ____, ____, ____, ____

Check ratios:
- 21 ÷ 7 = 3
- 63 ÷ 21 = 3
- 189 ÷ 63 = 3
- 567 ÷ 189 = 3

Common ratio: ×3

Geometric sequence.

Continue:
- 567 × 3 = 1701
- 1701 × 3 = 5103
- 5103 × 3 = 15309
- 15309 × 3 = 45927
- 45927 × 3 = 137781

Sequence: 7, 21, 63, 189, 567, 1701, 5103, 15309, 45927, 137781

Type: Geometric

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#### 5. 5, 10, 20, 35, 55, ____, ____, ____, ____, ____

Check differences:
- 10 − 5 = 5
- 20 − 10 = 10
- 35 − 20 = 15
- 55 − 35 = 20

Differences: 5, 10, 15, 20 → increasing by 5 each time

So next differences: 25, 30, 35, 40, 45

Now add:
- 55 + 25 = 80
- 80 + 30 = 110
- 110 + 35 = 145
- 145 + 40 = 185
- 185 + 45 = 230

Sequence: 5, 10, 20, 35, 55, 80, 110, 145, 185, 230

Type: Neither (second-order pattern — differences increase linearly)

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#### 6. 70, 69, 67, 64, 60, ____, ____, ____, ____, ____

Check differences:
- 70 → 69 (−1)
- 69 → 67 (−2)
- 67 → 64 (−3)
- 64 → 60 (−4)

So decreasing by: −1, −2, −3, −4 → next: −5, −6, −7, −8, −9

Continue:
- 60 − 5 = 55
- 55 − 6 = 49
- 49 − 7 = 42
- 42 − 8 = 34
- 34 − 9 = 25

Sequence: 70, 69, 67, 64, 60, 55, 49, 42, 34, 25

Type: Neither (decreasing by increasing amounts)

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#### 7. 1, 4, 9, 16, 25, ____, ____, ____, ____, ____

These are perfect squares:
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25

Next: 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100

Sequence: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Type: Neither (quadratic pattern — squares)

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Part 2: Write the next five terms of each pattern, given the rule and starting number(s)

#### 8. Rule: ×2, Starting number: 6

Start with 6, multiply by 2 each time.

- 6 × 2 = 12
- 12 × 2 = 24
- 24 × 2 = 48
- 48 × 2 = 96
- 96 × 2 = 192

Next five terms: 12, 24, 48, 96, 192

This is a geometric sequence with common ratio 2.

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✔ Final Answers Summary

#### Part 1: Continue the patterns

| # | Sequence | Next Terms | Type |
|---|--------|------------|------|
| 1 | 24, 34, 33, 43, 42 | 52, 51, 61, 60, 70 | Neither |
| 2 | 1, 1, 2, 3, 5 | 8, 13, 21, 34, 55 | Neither |
| 3 | 76, 69, 62, 55, 48 | 41, 34, 27, 20, 13 | Arithmetic |
| 4 | 7, 21, 63, 189, 567 | 1701, 5103, 15309, 45927, 137781 | Geometric |
| 5 | 5, 10, 20, 35, 55 | 80, 110, 145, 185, 230 | Neither |
| 6 | 70, 69, 67, 64, 60 | 55, 49, 42, 34, 25 | Neither |
| 7 | 1, 4, 9, 16, 25 | 36, 49, 64, 81, 100 | Neither |

#### Part 2: Rule-based pattern

8. Rule: ×2, Start: 6
→ 12, 24, 48, 96, 192

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