# Linear sequences

##### Intros

###### Lessons

##### Examples

###### Lessons

**Using the formula to find the sequences**

You are given that the nth term of a sequence is

2n - 1

Write the first 4 terms of the sequence.**Finding the common difference, first few terms, and nth term**

Consider the linear sequence:

2, 5, 8, 11, 14, ... - Consider the linear sequence:

10, 8, 6, 4, 2, ... **Using the nth term formula and classifying unknown terms**

Consider the linear sequence:

1, 6, 11, 16, 21, ...

- Consider the linear sequence:

11, 7, 3, -1, -5, ...

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###### Topic Notes

In this section we will learn about finding the common difference, finding the next few terms of the sequences, and finding the formula for the $n$th term.

Look at the terms and see how much they are increasing or decreasing from one term to another.

Add the term with the common difference

__Common difference (term to term rule)__Look at the terms and see how much they are increasing or decreasing from one term to another.

__Finding the next term__Add the term with the common difference

__Finding the $n$th term (position to term rule)__- Find the common difference
- Write a multiplication table for the common difference. Find the general term for it
- Find the difference of the two sequences. Add/Subtract the difference to the general term to get the nth term.

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