Which sequence has constant 2nd differences? (1 point)
a. {5, 11.5, 18.5, 24.5}
b. {0.5, 5, 12.5, 23}
c. {-0.5, 5, 13.5, 23}
d. {5, 13.5, 23, 34.5}
The sequence that has constant 2nd differences is
d. {5, 13.5, 23, 34.5}
To determine which sequence has constant 2nd differences, we need to find the differences between consecutive terms and then the differences between those differences.
For sequence a:
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
For sequence b:
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
For sequence c:
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
For sequence d:
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
Among the given sequences, the sequence with a constant 2nd difference is:
c. {-0.5, 5, 13.5, 23}
To determine which sequence has constant second differences, we need to calculate the differences between consecutive terms and then calculate the differences between those differences.
Let's calculate the differences for each sequence:
a. {5, 11.5, 18.5, 24.5}
Differences: {6.5, 7, 6}
Second differences: {0.5, -1}
b. {0.5, 5, 12.5, 23}
Differences: {4.5, 7.5, 10.5}
Second differences: {3, 3}
c. {-0.5, 5, 13.5, 23}
Differences: {5.5, 8.5, 9.5}
Second differences: {3, 1}
d. {5, 13.5, 23, 34.5}
Differences: {8.5, 9.5, 11.5}
Second differences: {1, 2}
Now let's examine the second differences for each sequence:
a. The second differences are {0.5, -1}. They are not constant.
b. The second differences are {3, 3}. They are constant.
c. The second differences are {3, 1}. They are not constant.
d. The second differences are {1, 2}. They are not constant.
Therefore, the sequence that has constant second differences is b. {0.5, 5, 12.5, 23}.