Question

Which polynomial sequence shows that the terms of the 2nd differences are constant? (1 point) Responses {3,7,13,21} left brace 3 comma 7 comma 13 comma 21 right brace {0,4,16,34} left brace 0 comma 4 comma 16 comma 34 right brace {2,6,11,14} left brace 2 comma 6 comma 11 comma 14 right brace {1,7,12,19}

Answer 1

To determine which polynomial sequence shows that the terms of the second differences are constant, we need to calculate the first and second differences for each sequence.

Let's analyze each option:

1. **Sequence: {3, 7, 13, 21}**
- First differences: 7-3 = 4, 13-7 = 6, 21-13 = 8
→ {4, 6, 8}
- Second differences: 6-4 = 2, 8-6 = 2
→ {2, 2} (constant)

2. **Sequence: {0, 4, 16, 34}**
- First differences: 4-0 = 4, 16-4 = 12, 34-16 = 18
→ {4, 12, 18}
- Second differences: 12-4 = 8, 18-12 = 6
→ {8, 6} (not constant)

3. **Sequence: {2, 6, 11, 14}**
- First differences: 6-2 = 4, 11-6 = 5, 14-11 = 3
→ {4, 5, 3}
- Second differences: 5-4 = 1, 3-5 = -2
→ {1, -2} (not constant)

4. **Sequence: {1, 7, 12, 19}**
- First differences: 7-1 = 6, 12-7 = 5, 19-12 = 7
→ {6, 5, 7}
- Second differences: 5-6 = -1, 7-5 = 2
→ {-1, 2} (not constant)

From the calculations, the only sequence for which the second differences are constant is:

**{3, 7, 13, 21}**.