**For Parent**

# Arithmetic Sequences

Arithmetic Sequences are an important concept in Grade 9 math. The concept is relatively simple – a sequence is a list of numbers, and an arithmetic sequence is a list of numbers where each number in the sequence is the sum of the two numbers before it. When these sequences are written on paper, they are written as an equation with a common difference. The equation for an arithmetic sequence looks like this:

## An Example of an Arithmetic Sequence Equation

For example:

In an arithmetic sequence, the equation is written as “a_n = a_1+ (n-1)d”, where “a_1” is the first term of the sequence, “n” is the number of terms in the sequence, and “d” is the common difference between each term.

For example – if the first term of the sequence is 2, and the common difference is 4, then the 5th term of the sequence is:

2 + (5 – 1)4

2 + (4)4

2 + 16

18

## Helping a 14 Year Old with Dyslexia to Understand Arithmetic Sequences

Dyslexia can present a unique set of challenges when it comes to understanding and applying Arithmetic Sequences. Here are some tips for helping a 14 year old with Dyslexia learn about this topic:

## Example 1: Learning the Term Names and What They Represent

One issue a 14 year old with Dyslexia might encounter while learning Arithmetic Sequences is understanding the terminology. The equation “a_n = a_1+ (n-1)d” is written with a lot of variable terms (“a_n”, “a_1”, “n”, “d”) and it might be hard to learn what each one represents.

To help the 14 year old learn these terms, it is important to explain each one one at a time in an interactive way. Create diagrams to illustrate what each term stands for, use real-world examples to help explain the concepts, and come up with physical and visual activities for the student to do that will help them learn and remember the terms.

## Example 2: Learning to Solve Equations

A 14 year old with Dyslexia might also have difficulty understanding how to solve equations for Arithmetic Sequences. To help them, start with understanding what the equation is asking and the steps needed to answer it. Provide visual examples of how to solve the equation, and then walk them through it step by step, breaking the problem up into smaller pieces to make it easier to understand. It is also important to give them ample practice opportunities. Provide worksheets, puzzles, and real-world problems and explain how the steps used to solve them relate to the equation and provide a supportive and comfortable learning environment.

## Example 3: Keeping Track of the Steps of the Problem

The last issue a 14 year old with Dyslexia might encounter is keeping track of the steps of the problem. It can be hard to remember what each step is, particularly when the reasoning behind each step is not understood. To help with this, discuss the steps of the problem before starting and break them down into more manageable chunks. As each step is taken, have the student repeat every step out loud and explain why it is needed. This will help them to learn about the steps, remember them for future problems, and build their confidence.

# An Example Arithmetic Sequence Equation: a_n = a_1 + (n-1)d

As a reference, here is an example of an Arithmetic Sequence equation:

a_n = a_1 + (n-1)d

For example, what is the 4th term of an Arithmetic Sequence with a_1 = 5 and d = 7?

Answer:

The 4th term of the Arithmetic Sequence is 5 + (4 – 1)7 = 5 + 27 = 32.

**For Youth**

Arithmetic Sequences are a special type of numbers, and the grade 9 math curriculum in Ontario covers them in detail. Arithmetical sequences are when a pattern of numbers is repeated over and over in an organized way.

To help explain arithmetic sequences, let’s use an example. Let’s say you have the numbers 2, 4, 6. That’s an arithmetic sequence, because those numbers are added by 2 each time. That’s why it’s called an arithmetic sequence, because the numbers have a special type of math relationship between them.

Now, let’s look at the equation for an arithmetic sequence. It’s often written like this:

An = A1 + (n – 1) d

This is read as ‘a sub n equals a sub 1 plus n minus one times d.’

In this equation, A1 is the first number in the sequence. ‘n’ is the total amount of numbers in the sequence, and ‘d’ is the difference between each number.

To help you understand, let’s look at an example.

Let’s say our A1 is 2 and our d is 2. That means our sequence is 2, 4, 6.

To figure out the total amount of numbers in the sequence, the equation would look like this:

An = 2 + (n – 1)(2)

This means that ‘n’ equals 3. So, in this sequence there are three numbers.

Because you have Dyslexia, it might be a little harder for you to understand some of the tricky parts of arithmetic sequences. That’s okay though! There are lots of different strategies that you can use to make math easier.

For example, you can break down the equation step-by-step. This can help you make sure that you understand each part of the equation, before moving on to the next step. It can also help you to get an overall picture of what the equation is doing.

You can also use visual aids to help you understand equations. Drawing pictures or making diagrams can help you understand equations better, and make it easier to remember.

The most important thing is to keep practicing. Arithmetic sequences can be confusing at first, but if you keep trying, you will eventually get the hang of it.