GED Math: Calculating Theater Seats with Arithmetic Sequence Partial Sums

Identifying the Arithmetic Sequence

• 📌 The problem describes a theater with seats arranged in rows, forming an arithmetic sequence.
• 💡 The first row has 11 seats, the second has 13, the third has 15, and so on, indicating a common difference of 2 seats per row.

Calculating the 20th Term

• 🎯 To find the total seats in 20 rows, we first need to determine the number of seats in the 20th row.
• 🔑 Using the formula for the nth term of an arithmetic sequence (a_n = a_1 + (n-1)d), with a_1 = 11, n = 20, and d = 2, the 20th term is calculated as 11 + (20-1)*2 = 11 + 38 = 49 seats.

Finding the Total Number of Seats

• 📊 The partial sum of an arithmetic sequence formula is used to find the total number of seats.
• ⚡ The formula is S_n = (a_1 + a_n) / 2 * n, where a_1 is the first term, a_n is the last term, and n is the number of terms.
• ✅ Plugging in the values: S_20 = (11 + 49) / 2 * 20 = 60 / 2 * 20 = 30 * 20 = 600 seats.
• 💡 Therefore, there are a total of 600 seats in the theater across all 20 rows.