An auditorium has 49 rows of seats. The first row contains 40 seats. As you move to the rear of the auditorium, each row has 3 more seats than the previous row.
-How many seats are in the auditorium?
This is an arithmetic series
Sum(n) = (n/2)[2a + (n-1)d]
where a is the first term
n is the number of terms
d is the common difference, and
Sum(n) is the sum of the n terms
So you want Sum(49)
with a=40, d=-3 and n = 49
substitute
To determine the total number of seats in the auditorium, you need to find the number of seats in each row and then sum them up.
Given that the first row contains 40 seats and each subsequent row has 3 more seats than the previous row, you can use this pattern to calculate the number of seats in each row.
Let's break it down:
1st row: 40 seats
2nd row: 40 + 3 = 43 seats
3rd row: 43 + 3 = 46 seats
...
49th row: (49-1) x 3 + 40 = 3 x 48 + 40 = 144 + 40 = 184 seats
Now that you have the number of seats in each row, you can sum them up to find the total number of seats in the auditorium. To do this, you can use the formula for the sum of an arithmetic sequence:
Sum = (n/2) x (first term + last term)
In this case, the first term is 40, and the last term is 184. Since there are 49 rows, n = 49.
Sum = (49/2) x (40 + 184) = 24.5 x 224 = 5,456
Therefore, the auditorium has a total of 5,456 seats.