Question

Which polynomial sequence shows that the terms of the 2nd differences are constant? (1 point)
Responses

{2,6,11,14}

{1,7,12,19}

{−6,−1,14,39}

{0,4,16,34}

Answer 1

To determine which polynomial sequence has constant second differences, we can calculate the first and second differences of each sequence provided.

1. **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)

2. **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)

3. **Sequence**: {−6, −1, 14, 39}
- First differences: -1 - (-6) = 5, 14 - (-1) = 15, 39 - 14 = 25 → {5, 15, 25}
- Second differences: 15 - 5 = 10, 25 - 15 = 10 → {10, 10} (constant)

4. **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)

The only sequence that exhibited constant second differences is **{−6, −1, 14, 39}**.