Geometric Series Challenges: Find Ratios & Calculate Totals

A car's value depreciates by 20% each year. If the car's initial value is $20,000, what will its value be after 3 years? Determine the common ratio and apply the series formula to find the final value.

• $10,240

• $8,000

• $12,000

• $15,360

A bacteria culture doubles in size every hour. If the initial number of bacteria is 500, how many will there be after 5 hours? Identify the common ratio and calculate the total using the geometric series formula.

• 4000

• 8000

• 32000

• 16000

A bank offers a savings account that compounds interest at a rate of 5% per year. If you deposit $1,000, how much will you have after 4 years? Use the geometric series formula to find the total amount.

• 1300.00

• 1100.00

• 1215.51

• 1000.00

A video game character earns 100 points in the first level and then earns 150% of the previous level's points in each subsequent level. How many points will the character earn after 4 levels? Determine the common ratio and apply the series formula.

• 900

• 750

• 600

• 812.5

A tree grows 3 inches in the first year and then grows 150% of its previous year's growth each subsequent year. How tall will the tree be after 3 years? Find the common ratio and use the geometric series formula to calculate the height.

• 10.5 inches

• 14.25 inches

• 12 inches

• 16 inches

A company’s profit increases by 10% each quarter. If the profit in the first quarter is $5,000, what will the profit be in the fourth quarter? Determine the common ratio and apply the series formula to find the profit.

• 6655

• 7500

• 8000

• 6000

A cell phone plan offers a data package that increases by 25% each month. If the initial data limit is 2GB, how much data will be available after 6 months? Identify the common ratio and calculate the total using the geometric series formula.

• 10.25 GB

• 12.50 GB

• 16.42 GB

• 20.00 GB

A population of fish in a lake increases by 30% each year. If there are currently 1,000 fish, how many will there be after 2 years? Determine the common ratio and apply the series formula to find the population size.

• 1200

• 1690

• 1500

• 2000

A loan has an interest rate of 8% compounded annually. If you borrow $10,000, how much will you owe after 5 years? Use the geometric series formula to calculate the total amount owed.

• 13500.50

• 14693.28

• 12000.00

• 15800.75

A subscription service charges $10 for the first month and increases the fee by 20% each month. How much will you pay in total after 4 months? Identify the common ratio and apply the series formula to find the total cost.

• 53.68

• 40.00

• 45.00

• 60.00