Solve the problem.
-The number of students in a school in year $n$ is estimated by the model $a _ { n } = 7 n ^ { 2 } + 14 n + 85$. Write a sequence showing how many students are in the school in each of the first three years.
A) $120,155,204$
B) $113,141,190$
C) $106,141,190$
D) $106,141,169$

Question

Quizplus · Accepted Answer

To find out the number of students in the first three years, we need to plug in 1, 2, and 3 for n in the given equation.
For n = 1, 
$a_1 = 7\cdot 1^2 + 14\cdot 1 + 85 = 106$
For n = 2, 
$a_2 = 7\cdot 2^2 + 14\cdot 2 + 85 = 141$
For n = 3, 
$a_3 = 7\cdot 3^2 + 14\cdot 3 + 85 = 190$
Therefore, the sequence showing how many students are in the school in each of the first three years is 106, 141, and 190, which matches option C.

Solve the Problem nnn Is Estimated by the Model an=7n2+14n+85a _ { n } = 7 n ^ { 2 } + 14 n + 85an​=7n2+14n+85

Solve the Problem $n$ Is Estimated by the Model $a _ { n } = 7 n ^ { 2 } + 14 n + 85$