Test questions for real-world arithmetic series problems

📚 Quick Study Guide

• ➕ An arithmetic series is the sum of the terms of an arithmetic sequence.
• 🔢 The common difference ($d$) is the constant difference between consecutive terms.
• 📝 The $n^{th}$ term of an arithmetic sequence is given by: $a_n = a_1 + (n-1)d$, where $a_1$ is the first term.
• 📈 The sum ($S_n$) of the first $n$ terms of an arithmetic series is given by: $S_n = \frac{n}{2}(a_1 + a_n)$ or $S_n = \frac{n}{2}[2a_1 + (n-1)d]$.
• 💡 To solve real-world problems, identify $a_1$, $d$, and $n$ from the problem statement.

🧪 Practice Quiz

1. What is the sum of the first 20 terms of the arithmetic series where the first term is 3 and the common difference is 5?
   1. 650
   2. 1010
   3. 950
   4. 1060
2. A theater has 30 rows of seats. The first row has 20 seats, the second row has 22 seats, the third row has 24 seats, and so on. How many seats are there in total?
   1. 1650
   2. 1770
   3. 1560
   4. 1890
3. A construction company is building a staircase. The first step requires 10 bricks, the second step requires 12 bricks, the third step requires 14 bricks, and so on. If there are 15 steps, how many bricks are needed in total?
   1. 420
   2. 330
   3. 270
   4. 390
4. John saves $50 in January, $60 in February, $70 in March, and so on. If he continues this pattern, how much will he have saved by the end of December?
   1. $1020
   2. $660
   3. $1140
   4. $1320
5. An auditorium has 25 rows. The first row has 15 seats, and each subsequent row has 2 more seats than the previous row. How many seats are in the auditorium?
   1. 1275
   2. 1125
   3. 1050
   4. 900
6. A pile of logs has 25 logs on the bottom row, 24 logs on the second row, 23 logs on the third row, and so on, until there is only 1 log on the top row. How many logs are in the pile?
   1. 300
   2. 325
   3. 275
   4. 350
7. A student is preparing for a marathon. In the first week, they run 10 miles, in the second week, they run 12 miles, in the third week, they run 14 miles, and so on. If they continue this pattern for 10 weeks, how many miles will they have run in total?
   1. 190
   2. 200
   3. 220
   4. 240