Mastering Geometric Sequences and Real-World Problems

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

• $15,000

• $10,240

• $8,000

• $12,500

A bacteria culture doubles in size every hour. If you start with 500 bacteria, how many will there be after 5 hours?

• 4000

• 16000

• 20000

• 8000

A geometric sequence starts with 3 and has a common ratio of 4. What is the 5th term of the sequence?

• 256

• 1024

• 512

• 768

A tree grows 1.5 meters in the first year and then grows 1.5 times its height each subsequent year. How tall will the tree be after 4 years?

• 5.0625 meters

• 10.125 meters

• 7.5 meters

• 3.0 meters

A savings account earns 5% interest compounded annually. If you deposit $1,000, how much will you have in the account after 3 years?

• 1050.25

• 1157.63

• 1200.00

• 1100.50

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 in the 4th level?

• 337

• 400

• 250

• 300

A geometric sequence has a first term of 2 and a common ratio of 3. What is the sum of the first 4 terms?

• 54

• 80

• 30

• 100

A population of rabbits increases by 30% each month. If there are initially 200 rabbits, how many will there be after 2 months?

• 400

• 250

• 338

• 300

A company’s profit is modeled by a geometric series where the first year profit is $50,000 and it increases by a factor of 1.2 each year. What will be the profit in the 5th year?

• $103,680

• $120,000

• $80,000

• $90,000

A cell phone plan offers a monthly fee of $30 with an additional charge of $5 for each extra gigabyte used. If a user starts with 2GB and uses 3GB more each month, how much will the user pay in the 6th month?

• $90

• $105

• $75

• $120