Lesson Worksheet: Applications of Geometric Sequences and Series Mathematics

In this worksheet, we will practice solving real-world applications of geometric sequences and series, where we will find the common ratio, the nth term explicit formula, the order and value of a specific sequence term, and the sum of given number of terms.


After falling, a rubber ball bounces back to 14 of its previous height. Given that the ball fell from a height of 653 cm above the ground, find, to the nearest integer, the height it would reach after its second bounce.


A man sent a message to two of his friends, and each of them then sent the same message to another two friends and so on. Find the number of people who got the message the sixth time it was sent given that each person received the message only once.


Mason saves $20 every month in an account that pays an annual interest rate of 4% compounded monthly.

How much will be in Mason’s account after 4 years of regular saving? Give your answer to the nearest cent.

If the interest was compounded quarterly, how much would be in the account after 4 years?


A water tank had 1,778 liters of water. The volume of the water decreased by 14, 28, and 56 liters over the next three days, respectively. How long will it take the tank to be empty given the water volume decreases following the same pattern?


The number of students in a school increases by 10% every year and there are currently 2,988 students. How many students will the school have after 6 years?


On the first day, 42 liters of water are poured into a tank. Every day thereafter, three times as much water is poured into the tank as was poured on the previous day. On which day are 1,134 liters poured into the tank?

  • Aday 4
  • Bday 5
  • Cday 3
  • Dday 6
  • Eday 27


A gold mine produced 2,257 kg in the first year but production decreased by 14% annually. Find the amount of gold produced in the third year and the total across all 3 years. Give the answers to the nearest kg.

  • Aπ‘Ž=44, 𝑆=2,617
  • Bπ‘Ž=1,436, 𝑆=5,867
  • Cπ‘Ž=1,669, 𝑆=4,198
  • Dπ‘Ž=6, 𝑆=2,617
  • Eπ‘Ž=1,669, 𝑆=5,867


Chloe joined a company with a starting salary of $28,000. She receives a 2.5%β€Ž salary increase after each full year in the job.

The total Chloe earns over 𝑛 years is a geometric series. What is the common ratio?

Write a formula for π‘†οŠ, the total amount in dollars that Chloe earns in 𝑛 years at the company.

  • A𝑆=1,120,000(1.025βˆ’1)
  • B𝑆=58,947(1.475βˆ’1)
  • C𝑆=18,667(2.5βˆ’1)
  • D𝑆=28,000(1βˆ’1.025)
  • E𝑆=1,120,000(1βˆ’0.975)

After 20 years with the company, Chloe leaves. Use your formula to calculate the total amount she earned there.

Explain why the actual amount she earned will be different from the amount calculated using the formula.

  • AThe value of the dollar varies with time.
  • BShe spent part of the money within the 20 years.
  • CThe actual amount will have a different starting value compared to the amount calculated using the formula.
  • DWhen necessary, the new annual salary will be rounded.
  • EThe actual amount will have a different percentage compared to the amount calculated using the formula.


A ball fell vertically downward from a height of 270 cm above the ground. Each time the ball touches the ground, it bounces 49 of the previous distance. Find the falling distance when the ball touches the ground at the fourth time. Then find the total distance the ball covered during its motion. Give all answers to the nearest unit.

  • A24 cm, 702 cm
  • B24 cm, 486 cm
  • C11 cm, 702 cm
  • D26 cm, 945 cm
  • E46 cm, 945 cm


The production of an oil well every year is 20% less than the year before. Find the total number of barrels produced in the first eight years given the production in the first year was 28,450. Then, find the maximum production of the well. Give all answers to the nearest unit.

  • A112,418 barrels, 142,250 barrels
  • B118,384 barrels, 142,250 barrels
  • C568,993 barrels, 35,563 barrels
  • D568,999 barrels, 35,563 barrels

This lesson includes 24 additional questions and 171 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.