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## Writing Expression for Geometric Sequences

#### 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 nth 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  #### 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.

#### Math Skill Quizzes

This is quite a difficult skill to master for students.