# Variable Expressions Worksheets

A variable expression is just an algebraic expression that contains at least one variable. Variables, if we remember back, are symbols that replace unknown values. Terms in expressions that are only numbers are referred to as constants. The most common variable expressions that we work with are called binomials, they contain two terms. We will often work with polynomials which consists of more than one term as well. This is a huge section of worksheets that help both students and teachers to learn how to break down expressions or simple sequences to solve a problem that is presented to you. You will learn how to manipulate these terms to your own advantage and it will be a skill that you could use to solve many modern day scenarios.

### Aligned Standard: HSF-IF.A.3

- First Five Terms Step-by-step Lesson- You are given an expression and asked to find the first five terms of that expression; starting at 1.
- Guided Lesson - There is a real diversity of difficulty on this one.
- Guided Lesson Explanation - Some students will get lost with this skill, but if you get the students in a rhythm; it should all work out.
- Practice Worksheet - I tried to throw four difficult problems in here.
- Matching Worksheet - If students read the problems carefully, they should be able to quickly narrow down the correct choices.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We start off with very manageable sequences to help students build some confidence.

- Homework 1 - Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
- Homework 2 - The sequence 10, 20, 30... looks like 1, 2, 3...except each term is 10 times as large. So, the formula is 10n, where n represents the position of a term in the sequence. Check the first three terms.
- Homework 3 - Where n is the nth term, a1 is the first term, r is the common ratio, and n is the position of a term in the sequence 5, 10, 20, 40...

### Practice Worksheets

The practice sheets really start to make things a little bit demanding on students.

- Practice 1 - Find the common ratio between consecutive terms.
- Practice 2 - Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 3.
- Practice 3 - Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

### Math Skill Quizzes

This should be a fair assessment of where kids stand with the skill.

- Quiz 1 - Find the first two terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 2. 4(2)
^{n} - Quiz 2 - Make sure to double check the terms.
- Quiz 3 - There are more crazy geometric sequences here.

### What Are Variable Expressions and Sequences?

Variable expressions are just like any other algebraic expression, but in addition to having terms that may or may not have coefficients and constants, a variable is present. This variable is often presented as the variables x or y. In more common words, a combination of terms and operations that has at least one variable. These expressions come in handy when expressing a situation with unknown values.

Let's take a look at Susan's cupcake business to help us understand how variable expressions can be applied to the real world. Susan owns a cupcake bakery and gets a $2,500 in profit every day. She told her friend she would lend her $300, and she wants to find out how much she would be left with after lending her friend the money.

Let's say that Susan doesn't have a clear idea of the number of days she's working, so she needs to use a variable. We know that variables are a representation of an unknown value. Let's take the letter d as a variable. For finding Susan's profit before she lent the money, we will multiply her daily profit with the number of days she is working, hence- 2500x d. This can also be written as 2500d. This is known as a term which means that there are numbers, variables or numbers and variables multiplied together.

Now we need to consider the amount that will be deducted from Susan's profit i-e $300. For finding that, we will subtract the amount from Susan's daily profit, hence- 2500d-300. Since the 300 represents another term, the expression we have created is called variable expression!

In mathematics, a collection of objects which can also contain repetitions is called a sequence. Sequences, like sets, also have elements that are referred to as members or terms. The length of the sequence depends on the number of members. If it goes on forever, it is known as an infinite sequence. When there is a known number of members, it is known as a finite sequence.

Let's take an example: {2, 4, 6, 8, 10, 12 ...} The sequence contains ellipses; therefore, it will be called an infinite sequence. {a, b, c, d, e, f} With a definitive number shown, the sequence will be called a finite sequence.