Problem 71 - Algebra and Trigonometry

Question

A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?

Step-by-Step Solution

Answer

The total number of seats in this section of the stadium is the calculated sum \(S\) from step 3.

Step 1: Determine the first term, common difference, and number of terms

The first term \(a\) is the number of seats in the first row, which is 20. The common difference \(d\) is the increase in seats per row, which is 3. The number of terms \(n\) is the total number of rows, which is 38.

Step 2: Calculate the last term

The last term \(l\) can be calculated using the formula \(l = a + (n-1)*d\). Substitute \(a = 20\), \(d = 3\), and \(n = 38\) into the formula and solve for \(l\).

Step 3: Calculate the sum of the series

The sum \(S\) of the series can be calculated using the formula \(S = n/2 * (a + l)\). Substitute \(n = 38\), \(a = 20\), and the calculated \(l\) value into the formula and solve for \(S\).