Answer:
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
