7. a hockey arena has 10 920 seats. the first row of seats around the rink has 220 seats. the number of seats in each subsequent

Question

2 years ago

15

row increases by 16. how many rows of seats does the arena have?

1 answer:

Mazyrski [523] · Answer 1 · 2023-04-26T10:05:18+03:00

The number of rows in the arena is 26

<h3>How to determine the number of rows?</h3>

The hockey arena illustrates an arithmetic sequence, and it has the following parameters:

The number of rows (i.e. the number of terms) is calculated using:

$S_n = \frac{n}{2}(2a + (n -1) * d)$

So,we have:

$10920 = \frac{n}{2}(2 * 220 + (n -1) * 16)$

Evaluate the terms and factors

$21840 = n(440 + 16n -16)$

Evaluate the like terms

21840 = n(424+ 16n)

Expand

21840 = 424n + 16n^2

Rewrite as:

16n^2 + 424n - 21840 = 0

Using a graphical tool, we have:

n = 26

Hence, the number of rows in the arena is 26

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