These lessons help High School students to express and interpret geometric sequence applications.

**Related Pages**

Number Sequences

Linear Sequences

Geometric Sequences: n-th Term

Quadratic and Cubic Sequences

Examples, solutions, videos, and lessons to help High School students learn to choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A. Factor a quadratic expression to reveal the zeros of the function it defines.

B. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

C. Use the properties of exponents to transform expressions for
exponential functions. For example, the expression 1.15^{t }can
be rewritten as (1.15^{1/12})^{12t} ≈
1.012^{12t} to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.

Use properties of exponents (such as power of a power, product of powers, power of a product, and rational exponents, etc.) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay.

**Common Core: HSA-SSE.B.3c**

**Geometric Sequences Word Problems**

**Examples:**

- Bruno has 3 pizza stores and wants to dramatically expand his franchise nationwide. If the number of stores he owns doubles in number each month, what month will he launch 6,144 stores?
- On January 1, Abby’s troop sold three boxes of Girl Scout cookies online. Their daily goal
is to sell double the number of boxes as the previous day. At this rate, how many boxes will
they sell on day 7?

If this pattern continues, on what day will they sell 24,576 boxes of cookies?

**Compounding Interest and other Geometric Sequence Word Problems**

**Examples:**

- Suppose you invest $1,000 in the bank. You leave the money in for 3 years, each year getting 5% interest per annum. How much money do you have in the bank after 3 years?
- You invest $5000 for 20 years at 2% p.a. How much will we end up with? How does this change if the interest is given quarterly? monthly?
- If I can invest at 5% and I want $50,000 in 10 years, how much should I invest now?
- I decide to run a rabbit farm. I have 50 rabbits. The rabbit grows at 7% per week. How many will I have in 15 weeks?

**Geometric sequence - salary**

**Example:**

You land a job as a police officer. Your salary for the first year is $43,125. You will receive
7% increase every year. How much will your salary be at the start of year six?

**Solve Word Problems using Geometric Sequences**

**Example:**

Wilma bought a house for $170,000. Each year, it increases 2% of its value.

a. Write the equation that represents the house’s value over time.

b. What will the house be worth in 10 years?

**Application of a Geometric Sequence**

**Example:**

Bouncing ball application of a geometric sequence

When a ball is dropped onto a flat floor, it bounces to 65% of the
height from which it was dropped. If the ball is dropped from 80 cm,
find the height of the fifth bounce.

**Population Growth and Compound Interest**

This video gives examples of population growth and compound interest. Remember these examples are variations on geometric sequence.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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