The successive differences of a sequence are shown in the image. What is the standard form of its related polynomial expression?

Question

(1 point)
Responses

An2+Bn+C

An4+Bn3+Cn2+Dn+E

An+B

An3+Bn2+Cn+D

Answer 1

To determine the standard form of the polynomial, we need to analyze the successive differences of the sequence given.

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

Since we do not have access to the image or the specific successive differences, please check the differences:

• If the first set of differences is constant, the answer is \( An + B \).
• If the second set of differences is constant, the answer is \( An^2 + Bn + C \).
• If the third set of differences is constant, the answer is \( An^3 + Bn^2 + Cn + D \).
• If the fourth set of differences is constant, the answer is \( An^4 + Bn^3 + Cn^2 + Dn + E \).

Based on the level of differences that are constant in your data, you can select the corresponding polynomial form.