Real-world examples of arithmetic sequences and their applications

📚 Quick Study Guide

• ➕ An arithmetic sequence is a list of numbers with a constant difference between consecutive terms.
• 🔢 The general formula for an arithmetic sequence is: $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
• 📅 Real-world examples include: simple interest calculations, theater seating arrangements, and stacking objects.
• 🌱 Understanding arithmetic sequences helps in predicting patterns and making informed decisions based on numerical progressions.

🤔 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 theater has 20 seats in the first row, 22 in the second, 24 in the third, and so on. How many seats are in the 10th row?
1. 36
2. 38
3. 40
4. 42
3. If you deposit $100 into a savings account that earns simple interest of 5% per year, how much will you have in the account after 5 years? (This forms an arithmetic sequence of yearly balances)
1. $120
2. $125
3. $130
4. $135
4. A stack of bricks has 50 bricks in the bottom row, 48 in the second row, 46 in the third row, and so on. How many bricks are in the 10th row?
1. 30
2. 32
3. 34
4. 36
5. Find the 15th term of the arithmetic sequence with $a_1 = 5$ and $d = 3$.
1. 44
2. 46
3. 47
4. 49
6. A baker stacks cupcakes in the shape of a pyramid. The bottom layer has 16 cupcakes, the next layer has 14, then 12, and so on. If this continues until the top layer has 2 cupcakes, how many layers are there?
1. 6
2. 7
3. 8
4. 9
7. What is the sum of the first 10 terms of the arithmetic sequence: 1, 4, 7, 10, ...?
1. 135
2. 140
3. 145
4. 150