## Writing Expression for Geometric Sequences

#### Aligned To Common Core Standard:

**High School** - HSA-SSE.B.4

How to Write Expressions for Geometric Sequences -
Understanding patterns in a numeric data set is one of the most important concepts when studying number systems. Students have to grasp the concept of a variety of different sequences and series types, such as arithmetic sequences, harmonic sequences, Fibonacci numbers, and geometric sequences.
A geometric sequence is one that students are introduced to after arithmetic sequences. In arithmetic sequences, there is a common difference "d" between two consecutive terms. The difference can either be positive or negative. In a geometric sequence, you can find the next term by multiplying a term by a common ration "r."
To write an expression that defines a particular geometric sequence, you will have to bring into use its recursive formula which is given by;
a(n)=k x r^{(n-1)}
The formula can be used to find any n^{th} term of the sequence.
Here; k = first term of the sequence, r = the common ratio, n = required term number
So, how do you find the expression?
Consider the following sequence;
54, 18, 6, ...
**Step 1: Identify the Common Ratio** - To find the common ratio between two consecutive terms, you must divide the second term in the sequence from the first term; r = (second term)/(first term)
To check if the ratio is the same throughout, you can then divide the third term of the sequence from the second term. In this case, r is 1/3.
**Step 2: Use the Recursive Formula** - Now that you know the ratio between the terms, you can easily create an expression by inserting the terms.
a(n) = 54 [(1/3)] ^{(n-1)} The final expression can be used to find out any term in the sequence! These worksheets help students understand how to form and create an expression that represents a geometric sequence.

### Printable Worksheets And Lessons

- Expressions for
Sequences Step-by-step Lesson- You are given a sequence where
we would like you to write it as an expression.

- Guided Lesson
- This type of question will scare students at first, but eventually
becomes routine as the year goes on.

- Guided Lesson Explanation
- I like to use reverse numbers lines to help explain this at times.
The visuals help a great deal.

- Practice Worksheet
- We work on this skill until you have a really good handled on
what is going on with it.

- Matching Worksheet
- Match the patterns to the expressions that narrate them.

#### Homework Sheets

It was puzzling to see this standard at first. It has such a short scope and little real world application.

- Homework 1 - Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
- Homework 2 - Carefully plan each step of your sequence.
- Homework 3 - Find the common ratio between consecutive terms.

#### Practice Worksheets

I took these sheets and made them work in a pattern to help kids along.

- Practice 1 - This is a pot of gold.
- Practice 2 - More luck of the Irish for you.
- Practice 3 - A little more work is required here.

#### Math Skill Quizzes

This is quite a difficult skill to master for students.