Question

Please help! Need soon!

The first row of a movie theater has 15 seats and 3 additional seats in each subsequent row. How many seats are in the 14th row? How many seats in total are in the first 14 rows?

Answer 1

There are 54 seats in 14th row,

In the first 14th row the total seats are 483.

Explanation:

Given,

The number of seats in first row = 15,

Also, 3 additional seats in each subsequent row,

⇒ The seats in second row = 15 + 3 = 18,

⇒ The seats in third row = 18 + 3 = 21,

⇒ The seats in fourth row = 21 + 3 = 24,

................................................, so on,........

Thus, the given situation can be written as an AP,

15, 18, 21, 24,...........

Having first term, a = 15,

Common difference, d = 3,

Thus, the number of seats in 14th row,

`a_(14)=a+(14-1)3=15+13(3)=15+39=54`

Also, the total number of seats in total in the first 14th seats,

`S_(14)=(14)/(2)[2a+(14-1)d]=7(2* 15+13(3))=7(30+39)=7(69)=483`