Mastering Arithmetic Sequences: Sums & Formulas

A gardener plants a row of 5 trees. Each tree is planted 3 feet apart. How far apart are the first and last trees? Write the explicit formula for the distance between the trees.

• 15 feet

• 6 feet

• 12 feet

• 9 feet

A student saves $5 in the first week and increases his savings by $2 each week. How much will he have saved after 10 weeks? What is the sum of his savings for the first 10 weeks?

• 160

• 140

• 100

• 120

A book series has its first book released in 2010 and a new book is released every 2 years. In which year will the 6th book be released? Write the explicit formula for the year of release of the nth book.

• 2020

• 2018

• 2012

• 2022

A concert hall has 100 seats in the first row and each subsequent row has 5 more seats than the previous one. How many seats are there in the 8th row? What is the sum of the seats in the first 8 rows?

• 125 seats in the 8th row, 950 total seats in the first 8 rows.

• 135 seats in the 8th row, 1050 total seats in the first 8 rows.

• 130 seats in the 8th row, 1000 total seats in the first 8 rows.

• 140 seats in the 8th row, 1100 total seats in the first 8 rows.

A factory produces 50 toys in the first hour and increases production by 10 toys every hour. How many toys will be produced in the 5th hour? Write the explicit formula for the number of toys produced in the nth hour.

• 70

• 80

• 90

• 100

A runner completes 2 laps in the first minute and increases his laps by 1 lap every minute. How many laps will he complete in the 7th minute? What is the total number of laps completed in the first 7 minutes?

• 8 laps in the 7th minute; 35 total laps in the first 7 minutes.

• 5 laps in the 7th minute; 25 total laps in the first 7 minutes.

• 10 laps in the 7th minute; 42 total laps in the first 7 minutes.

• 6 laps in the 7th minute; 28 total laps in the first 7 minutes.

A staircase has 10 steps, and each step is 6 inches high. If you start at the ground level, how high will you be after climbing 7 steps? Write the explicit formula for the height after climbing n steps.

• 42 inches

• 36 inches

• 48 inches

• 54 inches

A savings account starts with $100 and earns $20 more each month. How much will be in the account after 12 months? What is the sum of the account balance for the first 12 months?

• $300 and $2400

• $400 and $3600

• $280 and $2400

• The account balance after 12 months is $340 and the sum of the account balance for the first 12 months is $2640.

A school has 200 students in the first grade and the number of students increases by 15 each year. How many students will be in the 5th grade after 4 years? Write the explicit formula for the number of students in the nth grade.

• 220

• 245

• 260

• 300

A bicycle shop sells 10 bikes in the first week and sells 3 more bikes each subsequent week. How many bikes will be sold in the 6th week? What is the total number of bikes sold in the first 6 weeks?

• In the 6th week, 30 bikes will be sold. The total number of bikes sold in the first 6 weeks is 120.

• In the 6th week, 20 bikes will be sold. The total number of bikes sold in the first 6 weeks is 90.

• In the 6th week, 15 bikes will be sold. The total number of bikes sold in the first 6 weeks is 75.

• In the 6th week, 25 bikes will be sold. The total number of bikes sold in the first 6 weeks is 105.