Use the image to answer the question.

Question

The successive differences of a sequence are shown in the image. What is the standard form of its
related polynomial expression?
(1 point)
An + B + C + Dn + E
4 n
3 n
2
An
3 + Bn
2 + Cn + D
An + B
An + Bn + C

Answer 1

To determine the standard form of the polynomial expression related to the given sequence from its successive differences, we can follow a systematic analysis based on the degree indicated by the differences.

• If the first differences are constant, the polynomial is linear \(An + B\).
• If the second differences are constant, the polynomial is quadratic \(An^2 + Bn + C\).
• If the third differences are constant, the polynomial is cubic \(An^3 + Bn^2 + Cn + D\).
• If the fourth differences are constant, the polynomial is quartic \(An^4 + Bn^3 + Cn^2 + Dn + E\).

Since I cannot see the image, please check:

• Determine how many times you need to take differences until you get a constant value.
• Based on that result, you can select the appropriate polynomial expression from the options given.

If you can provide details about the pattern of differences, I'd be happy to help deduce the polynomial expression!