Real-World Examples of Arithmetic Sequences Explained

📚 Quick Study Guide

• 🔢 An arithmetic sequence is a sequence where the difference between consecutive terms is constant. This constant difference is called the common difference, often denoted as $d$.
• ➕ The general formula for the $n^{th}$ term ($a_n$) of an arithmetic sequence is: $a_n = a_1 + (n-1)d$, where $a_1$ is the first term and $n$ is the term number.
• 📈 You can determine the common difference ($d$) by subtracting any term from its subsequent term: $d = a_{n+1} - a_n$.
• 🧮 The sum of the first $n$ terms ($S_n$) of an arithmetic sequence is given by: $S_n = \frac{n}{2}[2a_1 + (n-1)d]$ or $S_n = \frac{n}{2}(a_1 + a_n)$.

Practice Quiz

1. What is the common difference in the arithmetic sequence: 2, 6, 10, 14, ...?
   1. 2
   2. 3
   3. 4
   4. 5
2. A taxi charges an initial fee of $5.00 and $2.50 for each mile. What is the cost for a 5-mile ride?
   1. $12.50
   2. $15.00
   3. $17.50
   4. $20.00
3. A stack of bricks has 61 bricks in the bottom row, 58 in the second row, 55 in the third row, and so on until the top row has 10 bricks. How many rows are there?
   1. 15
   2. 16
   3. 17
   4. 18
4. Find the 10th term of the arithmetic sequence: 1, 4, 7, 10, ...
   1. 25
   2. 28
   3. 31
   4. 34
5. A theater has 20 rows of seats. The first row has 15 seats, the second row has 17 seats, the third row has 19 seats, and so on. How many seats are in the 20th row?
   1. 45
   2. 51
   3. 53
   4. 55
6. What is the sum of the first 20 natural numbers?
   1. 190
   2. 200
   3. 210
   4. 220
7. Sarah saves $100 in January, $120 in February, $140 in March, and so on. How much will she have saved in total by the end of December (12 months)?
   1. $1920
   2. $2280
   3. $2760
   4. $3120