Question

Mr. Stevens wrote two number patterns on the board.

Pattern 1: 5, 11, 17, 23, 29
Pattern 2: 16, 13, 10, 7, 4
He asked his students to find 2 new groups of numbers that use the same rules for the patterns shown. Which of the following groups of numbers use the same rules for the number patterns?

A.

3, 7, 11, 15, 19 and
65, 62, 59, 56, 53

B.

1, 7, 13, 19, 25 and
24, 21, 18, 15, 12

C.

4, 10, 16, 20, 24 and
27, 22, 17, 11, 6

D
.

6, 12, 24, 48, 96 and
3, 6, 9, 12, 15

Answer 1

To determine which of the given groups of numbers follows the same rules as the patterns shown, we need to analyze both patterns provided by Mr. Stevens:

**Pattern 1**: 5, 11, 17, 23, 29
- This sequence increases by 6 for each consecutive term.
- The pattern can be expressed as: \( a_n = 5 + (n-1) \times 6 \)

**Pattern 2**: 16, 13, 10, 7, 4
- This sequence decreases by 3 for each consecutive term.
- The pattern can be expressed as: \( b_n = 16 - (n-1) \times 3 \)

Now, let's look for similar patterns among the options provided.

### Option A:
**3, 7, 11, 15, 19**
- This increases by 4 for each consecutive term. \( a_n = 3 + (n-1) \times 4 \) (not the same as Pattern 1)

**65, 62, 59, 56, 53**
- This decreases by 3 for each consecutive term. \( b_n = 65 - (n-1) \times 3 \) (similar to Pattern 2)

This option does not match both patterns.

### Option B:
**1, 7, 13, 19, 25**
- This increases by 6 for each consecutive term. \( a_n = 1 + (n-1) \times 6 \) (not the same as Pattern 1)

**24, 21, 18, 15, 12**
- This decreases by 3 for each consecutive term. \( b_n = 24 - (n-1) \times 3 \) (similar to Pattern 2)

This option does not match both patterns.

### Option C:
**4, 10, 16, 20, 24**
- This increases by 6 for the first four terms and then by 4 to 24. Inconsistent with Pattern 1.

**27, 22, 17, 11, 6**
- This decreases by 5 for each consecutive term. \( b_n = 27 - (n-1) \times 5 \) (not the same as Pattern 2)

This option does not match both patterns.

### Option D:
**6, 12, 24, 48, 96**
- This does not follow a linear pattern as seen in Pattern 1.

**3, 6, 9, 12, 15**
- This increases by 3 for each consecutive term. Not the same as Pattern 2.

This option does not match both patterns.

### Conclusion:
None of the provided options (A, B, C, D) match the number patterns of Mr. Stevens based on the established rules of both an arithmetic increase and decrease. The problem may contain an oversight or may require re-evaluation of the groups presented.