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A section of a stadium is designed to hold 1485 fans. The first row will hold 40 seats, the second row will hold 45, the third will hold 50, and so on. If the seats in each row continue to increase in this way, how many rows should the section include?

Respuesta :

MathPhys

Answer:

18

Step-by-step explanation:

40 + 45 + 50 + ...

This is an arithmetic series with initial value of 40 and common difference of 5.

The sum of the first n terms of an arithmetic series is:

S = ½ n (2a + (n−1) d)

Given that S = 1485, a = 40, and d = 5:

1485 = ½ n (2 (40) + (n−1) (5))

2970 = n (80 + 5n − 5)

2970 = n (75 + 5n)

2970 = 5n² + 75n

594 = n² + 15n

0 = n² + 15n − 594

0 = (n + 33) (n − 18)

n = -33 or 18

Since n > 0, n = 18. The section will need 18 rows.

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