Mastering Sum of Geometric Series: Real-World Applications

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? Use the geometric series formula to find the total depreciation.

• $8,000

• $12,000

• $15,360

• $10,240

A company invests $1,000 in a project that yields a return of 10% each year. How much will the total return be after 5 years? Calculate using the sum of the geometric series.

• 1,200.00

• 610.51

• 1,500.00

• 500.00

A tree grows 50% taller each year. If it starts at 2 meters, how tall will it be after 4 years? Use the geometric series to find the height.

• 6 meters

• 10.125 meters

• 12 meters

• 8.5 meters

A bank offers a savings account with an interest rate of 5% compounded annually. If you deposit $500, how much will you have after 6 years? Apply the geometric series formula to find the total amount.

• 500.00

• 750.00

• 600.00

• 670.05

A video game character earns 200 points in the first level and doubles the points in each subsequent level. How many points will the character earn after 5 levels? Use the geometric series to calculate the total points earned.

• 5200

• 6400

• 1600

• 4000

A population of bacteria doubles every hour. If you start with 100 bacteria, how many will there be after 3 hours? Use the geometric series to find the total population.

• 200

• 800

• 1600

• 400

A phone plan costs $30 for the first month and increases by 10% each month. What will be the total cost after 6 months? Apply the geometric series formula to find the total cost.

• 180.00

• 210.00

• 250.00

• 231.47

A ball is dropped from a height of 80 meters and bounces back to 75% of its height each time. How high will it bounce after the third bounce? Use the geometric series to calculate the height.

• 40 meters

• 25 meters

• 50 meters

• 33.75 meters

A light bulb's brightness decreases by 15% each hour. If it starts at 1000 lumens, what will its brightness be after 5 hours? Use the geometric series to calculate the remaining brightness.

• 443.7 lumens

• 500 lumens

• 750 lumens

• 300 lumens