Find a quadratic model for the sequence with the indicated terms.
$$a _ { 0 } = 7 , a _ { 2 } = 3 , a _ { 5 } = 12$$
A) $a _ { n } = n ^ { 2 } + 7$
B) $a _ { n } = n ^ { 2 } - 4 n + 7$
C) $a _ { n } = n ^ { 2 } - 7 n + 7$
D) $a _ { n } = n ^ { 2 } - 7 n + 4$
E) $\quad a _ { n } = n ^ { 2 } - n + 7$

Question

Quizplus · Accepted Answer

The correct quadratic model is $a_n = n^2 - 4n + 7$. This can be verified by substituting the given $n$ values into each option and checking against the given $a_n$ values. For option B, when $n = 0$, $a_n = 0^2 - 4(0) + 7 = 7$; when $n = 2$, $a_n = 2^2 - 4(2) + 7 = 3$; and when $n = 5$, $a_n = 5^2 - 4(5) + 7 = 12$, which matches the given sequence terms.

Find a Quadratic Model for the Sequence with the Indicated a0=7,a2=3,a5=12a _ { 0 } = 7 , a _ { 2 } = 3 , a _ { 5 } = 12a0​=7,a2​=3,a5​=12

Find a Quadratic Model for the Sequence with the Indicated $a _ { 0 } = 7 , a _ { 2 } = 3 , a _ { 5 } = 12$