Answer:
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
.
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](https://img.qammunity.org/2022/formulas/mathematics/high-school/qw67imbfe5ayfuzyy6ia6vsjvb9sf5w4ph.png)
Therefore, there are 8428 seats in all.