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##### Intros
###### Lessons
1. Linear Sequences Overview:
2. Common Difference
3. Finding the next few terms
4. $n$th term
5. Classifying unknown terms
##### Examples
###### Lessons
1. 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.
1. Finding the common difference, first few terms, and nth term
Consider the linear sequence:
2, 5, 8, 11, 14, ...
1. Find the common difference.
2. Find the next 4 terms.
3. Find the nth term.
2. Consider the linear sequence:
10, 8, 6, 4, 2, ...
1. Find the common difference.
2. Find the next 4 terms.
3. Find the nth term.
3. Using the nth term formula and classifying unknown terms
Consider the linear sequence:
1, 6, 11, 16, 21, ...

1. Find the nth term.
2. Find the 100th term.
3. Is 106 a term in the sequence?
4. Is 245 a term in the sequence?
4. Consider the linear sequence:
11, 7, 3, -1, -5, ...

1. Find the nth term.
2. Find the 15th term.
3. Is -103 a term in the sequence?
4. Is -205 a term in the sequence?
###### 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.
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)
1. Find the common difference
2. Write a multiplication table for the common difference. Find the general term for it
3. Find the difference of the two sequences. Add/Subtract the difference to the general term to get the nth term.