Grade 12 Arithmetic Sequences Word Problems

Grade 12 Arithmetic Sequences Word Problems

Read each word problem carefully and solve it using your knowledge of arithmetic sequences. Show all your work.

1. A high school auditorium has 20 rows of seats. The first row has 15 seats, and each subsequent row has 2 more seats than the row in front of it. How many seats are in the last row?

2. Sarah is saving money for a new laptop. She starts with $50 in her savings account and adds $15 each week. After 10 weeks, she will have $ . To reach her goal of $500, she needs to save for   weeks.

3. A stack of logs has 16 logs in the bottom layer, 15 logs in the second layer, and so on, with one less log in each layer. If there are 7 layers in total, how many logs are in the 5th layer?

4. A runner trains by increasing her distance each day. On the first day, she runs 3 km. On the second day, she runs 3.5 km. On the third day, she runs 4 km, and so on. If she continues this pattern, how far will she run on the 15th day?

5. A company's profit increases by $5000 each month. If their profit in the first month was $10,000, their profit in the 6th month will be $35,000.

6. A construction worker earns $25 for the first hour of work, and his hourly rate increases by $2 for each subsequent hour. If he works for 8 hours, what is his total earnings for the day?

7. A concert hall has 40 rows of seats. The first row has 10 seats, and each row after that has 3 more seats than the previous row. The total number of seats in the first 5 rows is  . The total number of seats in the entire concert hall is  .