Question

successive differences practice
complete this assessment to review what youve learned. it will not count toward your grade.
what are the 2nd differences of the sequence from the following polynomial?
$n^2 + n + 1$
(1 point)

Explanation:

Step1: Generate sequence terms

For \(n=1,2,3,4,5\):

• \(n=1\): \(1^2 + 1 + 1 = 3\)
• \(n=2\): \(2^2 + 2 + 1 = 7\)
• \(n=3\): \(3^2 + 3 + 1 = 13\)
• \(n=4\): \(4^2 + 4 + 1 = 21\)
• \(n=5\): \(5^2 + 5 + 1 = 31\)

Sequence: \(3, 7, 13, 21, 31\)

Step2: Calculate 1st differences

Subtract consecutive terms:

• \(7-3=4\)
• \(13-7=6\)
• \(21-13=8\)
• \(31-21=10\)

1st differences: \(4, 6, 8, 10\)

Step3: Calculate 2nd differences

Subtract consecutive 1st differences:

• \(6-4=2\)
• \(8-6=2\)
• \(10-8=2\)

2nd differences: \(2, 2, 2\)

Answer:

The 2nd differences are a constant value of 2.