Use the First and Second Differences of the First Five $$\begin{array} { l } a _ { 1 } = 0 \\a _ { n } = a _ { n - 1 } + 8 n\end{array}$$

Use the first and second differences of the first five terms of the given sequence to determine whether the sequence has a linear model, a quadratic model, or neither.
$$\begin{array} { l } a _ { 1 } = 0 \\a _ { n } = a _ { n - 1 } + 8 n\end{array}$$

A) first differences: $1,2,3,4$
second differences: 1, 1, 1
linear model

B) first differences: $8,24,56,120$
second differences: $16,32,64$
linear model

C) first differences: $8,16,32,64$
second differences: $8,16,32$
quadratic model

D) first differences: $8,24,56,120$
second differences: $16,32,64$
quadratic model

E) first differences: $8,16,32,64$
second differences: $8,16,32$
neither linear nor quadratic