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

Question

{−6, −1, 14, 39}
{0, 4, 16, 34}
{1, 7, 12, 19}
{2, 6, 11, 14}
8

Answer 1

To determine which polynomial sequence has constant second differences, we first calculate the first differences of each sequence, followed by the second differences.

Let's analyze each of the sequences given:

1. Sequence: {-6, -1, 14, 39}

   • First differences:
     • (-1) - (-6) = 5
     • 14 - (-1) = 15
     • 39 - 14 = 25
   • First differences: {5, 15, 25}
   • Second differences:
     • 15 - 5 = 10
     • 25 - 15 = 10
   • Second differences are constant.

2. Sequence: {0, 4, 16, 34}

   • First differences:
     • 4 - 0 = 4
     • 16 - 4 = 12
     • 34 - 16 = 18
   • First differences: {4, 12, 18}
   • Second differences:
     • 12 - 4 = 8
     • 18 - 12 = 6
   • Second differences are not constant.

3. Sequence: {1, 7, 12, 19}

   • First differences:
     • 7 - 1 = 6
     • 12 - 7 = 5
     • 19 - 12 = 7
   • First differences: {6, 5, 7}
   • Second differences:
     • 5 - 6 = -1
     • 7 - 5 = 2
   • Second differences are not constant.

4. Sequence: {2, 6, 11, 14}

   • First differences:
     • 6 - 2 = 4
     • 11 - 6 = 5
     • 14 - 11 = 3
   • First differences: {4, 5, 3}
   • Second differences:
     • 5 - 4 = 1
     • 3 - 5 = -2
   • Second differences are not constant.

Based on the calculations above, the sequence {-6, -1, 14, 39} shows that the second differences are constant (both equal to 10).

Thus, the answer is: {−6, −1, 14, 39}.