## [HELP? 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

Question

[HELP? 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?

0

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