Question

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

{1,7,12,19}
{
1
,
7
,
12
,
19
}
left brace 1 comma 7 comma 12 comma 19 right brace

{0,4,16,34}
{
0
,
4
,
16
,
34
}
left brace 0 comma 4 comma 16 comma 34 right brace

{−6,−1,14,39}
{
−
6
,
−
1
,
14
,
39
}

left brace negative 6 comma negative 1 comma 14 comma 39 right brace

{2,6,11,14}

Answer 1

To determine which polynomial sequence has constant second differences, we need to calculate the first and second differences for each given sequence.

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

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

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

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

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