Mastering Arithmetic Sequences: Formulas & Word Problems

1. A gardener plants a row of 5 trees. Each tree is planted 3 feet apart. Write a formula for the distance from the first tree to the nth tree. How far is the 10th tree from the first?

• 15 feet

• 30 feet

• 27 feet

• 20 feet

2. Sarah saves $5 in the first week, $10 in the second week, and continues to save in this pattern. Write a formula for the amount saved in the nth week. How much will she have saved by the 8th week?

• 30

• 40

• 50

• 25

3. A book series has its first book released in 2010, and each subsequent book is released every 2 years. Write a formula for the year the nth book is released. In what year will the 6th book be released?

• 2022

• 2020

• 2012

• 2018

4. A train leaves a station and travels 15 miles every hour. Write a formula for the distance traveled after n hours. How far will the train have traveled after 5 hours?

• 60 miles

• 90 miles

• 45 miles

• 75 miles

5. A concert ticket price starts at $20 and increases by $3 each year. Write a formula for the ticket price in the nth year. What will the ticket price be in the 4th year?

• $25

• $26

• $32

• $29

6. A staircase has 10 steps, and each step is 6 inches high. Write a formula for the height of the nth step. How high is the 7th step?

• 42 inches

• 54 inches

• 36 inches

• 48 inches

7. A factory produces 100 toys in the first month and increases production by 20 toys each month. Write a formula for the number of toys produced in the nth month. How many toys will be produced in the 5th month?

• 180

• 150

• 200

• 160

8. A swimming pool is filled with water at a rate of 50 gallons per hour. Write a formula for the total gallons of water after n hours. How many gallons will be in the pool after 8 hours?

• 300 gallons

• 500 gallons

• 400 gallons

• 200 gallons

9. A runner completes the first lap of a race in 2 minutes and decreases his time by 10 seconds for each subsequent lap. Write a formula for the time taken for the nth lap. How long will the 5th lap take?

• 70 seconds

• 100 seconds

• 80 seconds

• 90 seconds

10. A savings account starts with $100 and increases by $15 each month. Write a formula for the total amount in the account after n months. How much will be in the account after 12 months?

• $280

• $200

• $300

• $250