Question

A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row. How many seats are there in total

Answer 1

8428

Explanation:

According to the Question,

• Given, A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row.

We have a number sequence 13, 18, 23, ...

• We can say that this is an arithmetic sequence because of the common difference 'd', is equal to 5, and the first term 'a1' is equal to 13.

• The formula for the sum of an arithmetic sequence with n terms is given is
  `S_n= (n)/(2) [2a_1+(n-1)d]S` .

Substitute the given values into the equation to solve for the sum of the 56 rows of seats.

`S_56= (56)/(2)[2(13)+(56-1)(5)]\\S_(56)=28\left[26+275\right]\\S_(56)=28\left[301\right]\\S_(56)=8428`

Therefore, there are 8428 seats in all.