# Linear sequences

#### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

#### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

#### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

##### 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.