Mastering Geometric Sequences and Series Sums

A population of bacteria doubles every 3 hours. If the initial population is 500, how many bacteria will there be after 12 hours?

• 10000

• 2000

• 8000

• 4000

A car's value depreciates by 15% each year. If the car is currently worth $20,000, what will its value be after 4 years?

• $12,500.00

• $8,000.00

• $10,440.12

• $15,000.00

A bank offers an investment that pays 5% interest compounded annually. If you invest $1,000, how much will you have after 3 years?

• 1200.00

• 1157.63

• 1100.50

• 1050.75

A geometric sequence has a first term of 3 and a common ratio of 2. What is the 6th term of the sequence?

• 24

• 12

• 48

• 96

A tree grows 10% taller each year. If it is currently 5 meters tall, how tall will it be after 5 years?

• 12.5 meters

• 8.05 meters

• 6.5 meters

• 7.2 meters

The sum of the first n terms of a geometric series is given by $S_n = \frac{a(1 - r^n)}{(1 - r)}$. If $a = 4$ and $r = 0.5$, what is the sum of the first 5 terms?

• 8.00

• 10.25

• 7.75

• 6.50

A certain investment grows according to the formula $A = P(1 + r)^t$. If you invest $2,000 at an interest rate of 6% for 5 years, what will be the total amount?

• 2800.50

• 2500.00

• 2676.45

• 3000.00

A sequence starts with 2 and each term is multiplied by 3. What is the 4th term of this geometric sequence?

• 36

• 72

• 18

• 54

If a geometric series has a first term of 8 and a common ratio of 0.5, what is the sum of the first 6 terms?

• 15.75

• 30.25

• 20

• 10.5

A cell phone plan offers a monthly fee of $30 plus $5 for each additional gigabyte of data used. If you use 10 gigabytes in a month, what is the total cost?

• $90

• $50

• $80

• $70