Which Polynomial Sequence Shows That The Terms Of The 2nd Differences Are Constant? A.-6,-1,14,39 b.2,6,11,14 c. 0,4,16,34 d. 1,7,12,19

Answer 1

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

1. Option A: -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: 10, 10 → Constant

2. Option B: 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: 1, -2 → Not constant

3. Option C: 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: 8, 6 → Not constant

4. Option D: 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: -1, 2 → Not constant

From the calculations, only option A (-6, -1, 14, 39) shows constant second differences. Thus, the answer is A.