A theater has 56 rows of seats. If there are 13 seats in the 1st row, 18 in the 2nd row, 23 in the 3rd row . How many seats are there in total? Show and explain all work.

We can say that this is an arithmetic sequence because of the common difference.

The common difference, d, is equal to 4, and the first term is equal to 13.

The formula for the sum of an arithmetic sequence with n terms is given by

S_n= \frac{n}{2} [2a_1+(n-1)d]S

n

=

2

n

[2a

1

+(n−1)d]

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

S_56= \frac{56}{2}[2(13)+(56-1)(4)]S

5

6=

2

56

[2(13)+(56−1)(4)]

S_{56}=28\left[26+220\right]S

56

=28[26+220]

S_{56}=28\left[246\right]S

56

=28[246]

S_{56}=6888S

56

=6888

Therefore, there are 6,888 seats in all.

step-by-step explanation: s

3

step-by-step explanation: