Question

Stadium Construction: How many rows are in the corner section of a stadium containing 2040 seats if the first row has 10 seats and each successive row has 4 additional seats?

Short answer

There are 30 rows in the corner section of a stadium.

Step-by-step solution

Given Information 

A stadium containing 2040 seats. The first row has 10 seats and each successive row has 4 additional seats.

Sum formula 

first term = 10

each successive row has 4 additional seats. d=4

Total seats = 2040

Sum of seats = 2040

Use sum formula to solve for n

$$\begin{gathered} S_n=\frac{n}{2}\left(2a_1+(n-1)d\right) \\ {a}_1=10,d=4,sum=2040 \\ 2040=\frac{n}{2}\left(2\left(10\right)+(n-1)4\right) \\ 2040=\frac{n}{2}(4n+16) \end{gathered}$$

Solve for n 

$$\begin{gathered} 2040=\frac{n}{2}(4n+16) \\ Multiplyby2onbothsides \\ 4080=4n^2+16n \\ 0=4n^2+16n-4080 \\ divideby4 \\ {n}^2+4n-1020=0 \\ Usequadraticformula \\ n=\frac{-4\pm \sqrt{4^2-4·\hspace{0.17em}1·\left(-1020\right)}}{2·\hspace{0.17em}1} \\ n=\frac{-4\pm \hspace{0.17em}64}{2} \\ n=\frac{-4+\hspace{0.17em}64}{2}=30 \\ n=\frac{-4-\hspace{0.17em}64}{2}=-34 \end{gathered}$$

Number of rows cannot be negative .

There are 30 rows.