Which sequence has constant 2nd differences? (1 point)
{0.5,5,12.5,23}
{5,13.5,23,34.5}
{−0.5,5,13.5,23}
{5,11.5,18.5,24.5}
The correct sequence that has constant 2nd differences is:
{−0.5,5,13.5,23}
To determine which sequence has constant 2nd differences, we need to find the differences between consecutive terms, then find the differences between those differences.
Let's analyze each sequence:
1. {0.5, 5, 12.5, 23}
- Differences between consecutive terms: 5 - 0.5 = 4.5, 12.5 - 5 = 7.5, 23 - 12.5 = 10.5
- Differences between those differences: 7.5 - 4.5 = 3, 10.5 - 7.5 = 3
- The 2nd differences are constant (3).
2. {5, 13.5, 23, 34.5}
- Differences between consecutive terms: 13.5 - 5 = 8.5, 23 - 13.5 = 9.5, 34.5 - 23 = 11.5
- Differences between those differences: 9.5 - 8.5 = 1, 11.5 - 9.5 = 2
- The 2nd differences are not constant.
3. {-0.5, 5, 13.5, 23}
- Differences between consecutive terms: 5 - (-0.5) = 5.5, 13.5 - 5 = 8.5, 23 - 13.5 = 9.5
- Differences between those differences: 8.5 - 5.5 = 3, 9.5 - 8.5 = 1
- The 2nd differences are not constant.
4. {5, 11.5, 18.5, 24.5}
- Differences between consecutive terms: 11.5 - 5 = 6.5, 18.5 - 11.5 = 7, 24.5 - 18.5 = 6
- Differences between those differences: 7 - 6.5 = 0.5, 6 - 7 = -1
- The 2nd differences are not constant.
Therefore, the sequence that has constant 2nd differences is {0.5, 5, 12.5, 23}.