Question

Which polynomial sequence shows that the terms of the 2nd differences are constant? (1 point)
A. • {2, 6, 11, 14}
B.• {1, 7, 12, 19}
C. {0, 4, 16, 34}
D. {1-6, -1,14, 39}

Answer 1

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

1. **Sequence A: {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 B: {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 C: {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)

4. **Sequence D: {1, -6, -1, 14, 39}**
- First differences: \(-6-1 = -7\), \(-1-(-6) = 5\), \(14-(-1) = 15\), \(39-14 = 25\) → {-7, 5, 15, 25}
- Second differences: \(5-(-7) = 12\), \(15-5 = 10\), \(25-15 = 10\) → {12, 10, 10} (not constant)

After analyzing all sequences, **none of the given sequences exhibit constant second differences** needed to determine a polynomial of degree greater than or equal to 2.

If we had to select, it appears the option closest to having a constant pattern might be:

**None of the options truly shows constant second differences.**

However, if we reevaluate or assume option D is close to a polynomial of degree two due to its structure, but according to specifics, option D could not be concluded strictly as having the characteristic either.

Thus, none of these options meets the requirement of constant second differences, but **D** shows some potential for increasing polynomial sequences.