Question

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**.