Posted by **Riana** on Sunday, January 27, 2013 at 1:42am.

a hockey arena has a total seating capacity of 15690.the first row of seats around the rink has 262 seats. the number of seats in each subsequent row increases by 18. how many rows of seats are in the arena?

- math help! -
**Stephen**, Sunday, January 27, 2013 at 7:37am
Solve using aritmetic progression and quadratic equation, how?

Sum of AP = n/2(2a+(n-1)d)

Where n is the number of terms, ie in your case the number of rows of seats, 'a' is the number in the first row (a=262) and 'd' is the difference in the next row (d=18). Sum of AP is the number of seats in the arena (Sum=15690). Put this together and you get:

15690=n/2[2*262+(n-1)18]

18n^2+506n-31380=0

equation to: ax^2+bx+c,; a=18, b=506, c=-31380

Now comes the quadratic, solution to a quadratic =

[-b(+/-)Sqrt(b^2-4ac)]/2a

substitute the values of a,b anc from above into the quadratic and solve.

n=30.

Please always check your answer, in this case use sum of AP.

## Answer this Question

## Related Questions

- math - Determine the seating capacity of an auditorium with 10 rows of seats if ...
- Math - an auditorium has 50 rows of seats. THe first row has 20 seats, the row ...
- math (plz help) - In a movie theater, theater A has 30 seats in the first row. ...
- math - In a movie theater, Theater A has 30 seats in the first row. Each next ...
- Math - An auditorium has 30 rows of seats. It has 20 seats on the first row, 24 ...
- arithmetic - PLEASE I REALLY NEED HELP WITH THIS The seats at a local baseball ...
- Discrete Mathematics - Mathematical sequences can be used to model real life ...
- Math (arithmetic) - The total seating capacity of an auditorium is 1,065. The ...
- Math - An auditorium has 50 rows of seats. The first row has 20 seats, the ...
- math - In a movie theater, theater A has 30 seats in the first row. Each next ...

More Related Questions