Mastering Geometric Sequences: Nth Terms & Sums

A car's value decreases by 20% each year. If the car's initial value is $20,000, what will its value be after 3 years? Calculate the nth term for n=3.

• $10,240

• $12,000

• $8,000

• $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? Calculate the nth term for n=5.

• 32000

• 16000

• 1000

• 8000

A bank offers a savings account with an interest rate of 5% compounded annually. If you deposit $1,000, how much will you have after 4 years? Calculate the sum of the geometric series for the first 4 terms.

• 1215.51

• 1000.00

• 1100.00

• 1500.00

A tree grows 1.5 times its height each year. If the tree is 2 meters tall now, what will its height be after 4 years? Calculate the nth term for n=4.

• 6.0 meters

• 12.75 meters

• 8.5 meters

• 10.125 meters

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 6th level? Calculate the nth term for n=6.

• 759.375

• 800

• 450

• 600

A company’s profit increases by 10% each quarter. If the profit in the first quarter is $50,000, what will the profit be in the 3rd quarter? Calculate the nth term for n=3.

• 60000

• 55000

• 70000

• 60500

A geometric sequence starts with 3 and has a common ratio of 4. What is the sum of the first 5 terms of this sequence?

• 512

• 256

• 1024

• 1023

A population of fish in a lake increases by 25% each year. If there are currently 200 fish, how many will there be after 2 years? Calculate the nth term for n=2.

• 300

• 250

• 313

• 400

A geometric sequence has a first term of 10 and a common ratio of 3. What is the 4th term of the sequence? Calculate the nth term for n=4.

• 1000

• 270

• 81

• 90