Linear Sequences

What is a sequence?
A sequence is a list of numbers that follow a pattern.

What is a linear sequence?
A linear sequence is a list of numbers that increases or decreases by the same amount each time.

How to find the nth term of a linear sequence?

The following diagrams show how to find the nth term of a linear sequence. Scroll down the page for more examples and solutions on finding and using the nth term of a linear sequence.

Sequence Worksheets
Practice your skills With the following worksheets:

• Sequence & nth Term Worksheets

  Find the sequence & n^th term
  Find the sequence & n^th term
  Find the n^th term of a sequence with fractions

Steps to Find the nth Term

1. Find the Common Difference (d):
   Subtract any term from the term that follows it.
   d = (any term) - (the term before it)
   
2. Find the First Term (a):
   Identify the first term in the sequence.
   
3. Use the Formula:
   The nth term (a_n) of a linear sequence is given by:
   a_n = a + (n - 1)d
   Where:
   a_n is the nth term.
   a is the first term.
   n is the term number.
   d is the common difference.
   
4. Simplify the formula to get the nth term.

How to describe a linear sequence?
How to find the next few terms?
How to find the nth term?
How to use the nth term to find a term in the sequence?

Linear Sequences (nth term)
Finding and using the nth term of a linear sequence

• Show Step-by-step Solutions

The nth term of a simple linear sequence
linear sequences - finding the nth term.

• Show Step-by-step Solutions

Linear sequences

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Linear sequences 2

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Key Points:

• If the common difference (d) is positive, the sequence is increasing.
• If the common difference (d) is negative, the sequence is decreasing.
• The nth term formula allows you to find any term in the sequence.

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