Find a Quadratic Model for the Sequence with the Indicated $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$

Multiple Choice

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$

A) $a _ { n } = 3 n ^ { 2 } + 3$
B) $a _ { n } = 3 n ^ { 2 } - 5 n + 3$
C) $a _ { n } = 3 n ^ { 2 } - 3 n + 3$
D) $a _ { n } = 3 n ^ { 2 } - 3 n + 5$
E) $a _ { n } = n ^ { 2 } + 5 n + 3$