Due tomorrow] there are 10 rows in the center of the civic auditorium. each row has 2 more seats than the previous row. if there are 490 seats total in the center, how many seats are in the first row?

There are 40 seats in the first row

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 10 rows in the center of the Civic Auditorium

- Each row has 2 more seats than the previous row

- There are 490 seats total in the center

* Lets solve the problem

∵ Each row has 2 more seats than the previous row

∴ There is a constant difference between each two consecutive rows

- That means we can consider the number of seats in each row

 formed an arithmetic series

∵ In arithmetic series if the first term is a and the constant difference

  is d then any term in the series can get by the rule an = a + (n - 1)d ,

  where n is the position of the number in the series

∴ a1 = a , a2 = a + d , a3 = a + 2d , a4 = a + 3d ,

- The sum of n terms in the arithmetic series is Sn = n/2 [a + l] where

  l is the last term in the series

∵ There are 10 rows

∴ n = 10

∵ each row has 2 more seats than the previous row

∴ d = 2

∵ The first term is a

∴ The last term l = a + (10 - 1)d

∴ The last term l = a + 9d

∴ The last rerm l = a + 9(2) = a + 18

∵ The total seat in the 10s rows is 490 seats

∵ Sn = n/2 [a + l]

∴ 490 = 10/2 [a + a + 18] ⇒ simplify

∴ 490 = 5 [2a + 18]

- Divide both sides by 5

∴ 98 = 2a + 18

- Subtract 18 from both sides

∴ 80 = 2a

- Divide both sides by 2

∴ a = 40

∵ a is the number of seats in the first row

∴ There are 40 seats in the first row

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