Mastering Geometric Sequences and Common Ratios

A tree grows 2 feet in the first year and then grows 1.5 times its height each subsequent year. If the tree is 2 feet tall after the first year, what will its height be after the third year?

• 5 feet

• 6 feet

• 4.5 feet

• 3 feet

A bacteria culture doubles in size every hour. If there are initially 100 bacteria, how many will there be after 5 hours?

• 1600

• 4000

• 2400

• 3200

A car's value depreciates by 20% each year. If the car is worth $15,000 now, what will its value be in 3 years?

• $10,000

• $12,000

• $5,000

• $7,680

A savings account earns interest at a rate of 5% compounded annually. If you start with $1,000, how much will you have after 4 years?

• 1100.00

• 1300.00

• 1500.00

• 1215.51

A video game character earns 50 points in the first level and then earns 3 times that amount in each subsequent level. How many points will the character earn after completing the 5th level?

• 1000

• 2500

• 4050

• 1500

A population of fish in a lake is 200 and increases by a factor of 1.2 each year. What will the population be after 4 years?

• 300

• 500

• 350

• 415

A company produces 500 units of a product in the first month and increases production by a factor of 1.1 each month. How many units will be produced in the 6th month?

• 900

• 600

• 750

• 805

A loan of $1,200 is taken out with an interest rate of 10% compounded annually. How much will be owed after 2 years?

• 1200

• 1452

• 1320

• 1500

A plant grows 3 inches in the first month and then grows 1.5 times its height each month thereafter. How tall will the plant be after 4 months?

• 10.125 inches

• 12 inches

• 8.5 inches

• 6.75 inches

A sequence of numbers starts with 5 and each term is 4 times the previous term. What is the 5th term in this sequence?

• 320

• 640

• 1280

• 2560