An auditorium has 24 rows of seats. There are n = 23 seats in the first row, 24 seats in the second row, 25 seats in the third row, and so on. How many seats are there in all 24 rows?
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To find the total number of seats in all 24 rows, you can use the formula for the sum of an arithmetic series.
The first step is to find the number of terms in the series. In this case, the series starts with n = 23 and ends with n = 24 + 23 = 47, and they increase by a constant value of 1. So the number of terms, denoted as 'n', can be calculated using the formula:
n = (last term - first term) / common difference + 1
Here, the first term (a) is 23, the last term (l) is 47, and the common difference (d) is 1.
n = (47 - 23) / 1 + 1
n = 24
Now that we know there are 24 terms in the series, we can calculate the sum (S) using the formula:
S = (n/2) * (first term + last term)
Substituting the values we have:
S = (24/2) * (23 + 47)
S = 12 * 70
S = 840
Therefore, there are a total of 840 seats in all 24 rows of the auditorium.