Question

Which sequence has constant 2nd differences?(1 point)
Responses

{−0.5, 5, 13.5, 23}
{−0.5, 5, 13.5, 23}

{0.5, 5, 12.5, 23}
{0.5, 5, 12.5, 23}

{5, 11.5, 18.5, 24.5}
{5, 11.5, 18.5, 24.5}

{5, 13.5, 23, 34.5}

Answer 1

To determine which sequence has constant 2nd differences, we need to first find the 1st differences and then the 2nd differences for each sequence.

1. For the sequence **{−0.5, 5, 13.5, 23}**:
- 1st differences:
- 5 - (-0.5) = 5.5
- 13.5 - 5 = 8.5
- 23 - 13.5 = 9.5
- 2nd differences:
- 8.5 - 5.5 = 3
- 9.5 - 8.5 = 1
- (Not constant)

2. For the sequence **{0.5, 5, 12.5, 23}**:
- 1st differences:
- 5 - 0.5 = 4.5
- 12.5 - 5 = 7.5
- 23 - 12.5 = 10.5
- 2nd differences:
- 7.5 - 4.5 = 3
- 10.5 - 7.5 = 3
- (Constant!)

3. For the sequence **{5, 11.5, 18.5, 24.5}**:
- 1st differences:
- 11.5 - 5 = 6.5
- 18.5 - 11.5 = 7
- 24.5 - 18.5 = 6
- 2nd differences:
- 7 - 6.5 = 0.5
- 6 - 7 = -1
- (Not constant)

4. For the sequence **{5, 13.5, 23, 34.5}**:
- 1st differences:
- 13.5 - 5 = 8.5
- 23 - 13.5 = 9.5
- 34.5 - 23 = 11.5
- 2nd differences:
- 9.5 - 8.5 = 1
- 11.5 - 9.5 = 2
- (Not constant)

The only sequence with constant 2nd differences is **{0.5, 5, 12.5, 23}**.