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