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