Linear Sequences
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Examples, videos, solutions, activities and worksheets that are suitable for GCSE Maths.
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:
Steps to Find the nth Term
- Find the Common Difference (d):
Subtract any term from the term that follows it.
d = (any term) - (the term before it) - Find the First Term (a):
Identify the first term in the sequence. - Use the Formula:
The nth term (an) of a linear sequence is given by:
an = a + (n - 1)d
Where:
an is the nth term.
a is the first term.
n is the term number.
d is the common difference. - 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
The nth term of a simple linear sequence
linear sequences - finding the nth term.
Linear sequences
Linear sequences 2
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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