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

Question

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}.