An auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21, the third row has 22 seats, and so on, each row having one more seat than the previous row. How many seats are there all together?

a. write 2 different expressions for the total number of seats in the auditorium. One expression should use addition: the other should involve multiplication. Write an equation that uses these two expressions.
b. Solve the auditorium problem, explaining your reasoning.

Your problem is dealing with an arithmetic series, where

a=20 , d=1, and n = 50
Sum(n) = n/2[2a + (n-1)d]
= 25[40 + 49(1)]
= 2225

what are two different expressions for the total number of seats in the auditorium

2225

wrong though

^^^

Its pretty difficult. Not an answer just a comment.

a. To find the total number of seats in the auditorium, we can use addition and multiplication.

1. Addition expression: We can add up the number of seats in each row to find the total. The formula for the number of seats in each row can be represented as:

20 + 21 + 22 + ... + (20 + 49)

2. Multiplication expression: We can use the fact that the number of seats in each row is increasing by 1 seat for each subsequent row. The formula for the number of seats in the last row can be represented as:

20 + (20 + 1) + (20 + 2) + ... + (20 + 49)

Equation: We can set these two expressions equal to each other:

20 + 21 + 22 + ... + (20 + 49) = 20 + (20 + 1) + (20 + 2) + ... + (20 + 49)

b. To solve the auditorium problem, we need to find the sum of the numbers in the arithmetic sequence.

First, we can find the number of terms in the sequence using the formula for arithmetic sequence:

n = (Last term - First term) / Common difference + 1
n = (49 - 20) / 1 + 1
n = 30

Next, we can calculate the sum of the sequence using the formula for the sum of an arithmetic sequence:

S = (n/2)(First term + Last term)
S = (30/2)(20 + 20 + 49)
S = 15(40 + 49)
S = 15(89)
S = 1335

Therefore, there are a total of 1335 seats in the auditorium.