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1. Finding the General Term
of a Linear Sequence

2. What is a Linear Sequence?
• A linear sequence is a sequence where each term
increases or decreases by the same amount.
• This constant amount is called the common
difference.
• Example:
3, 6, 9, 12, 15, ...
Common difference = 3

3. General Term Formula
To find any term in a linear sequence, use:
• To find any term in a linear sequence, use:
• an=a1+(n−1)d
• Where:
• an= the nth term
• a = the first term
• d = the common difference
• n= the term number

4. Step-by-Step Example
• Sequence: 5, 8, 11, 14, ...
• First term a=5
• Common difference d=3
• Formula: an=a1+(n−1)d
• an=5+(n−1)3
• Simplify:
• an=5+3n−3=3n+2
• So, the general term is:
• an=3n+2

5. Why Find the General Term?
• Helps you find any term in the sequence without
listing all terms
• Useful in real-life situations like budgeting,
schedules, and planning

6. Practice Question 1
• Sequence: 2, 7, 12, 17, ...
• First term a=2
• Common difference d=5
• Find the general term
• Answer:
• an=2+(n−1)×5=5n−3

7. Practice Question 2
• Sequence: 20, 15, 10, 5, ...
• First term a=20
• Common difference d=−5
• Find the general term.
• Answer:
• an=20+(n−1)(−5)=−5n+25

8. Tips to Remember
• ✅ Always find first term and common difference
✅ Use the formula: an=a+(n−1)d
• ✅ Simplify the expression if needed
✅ Check your formula by plugging in small values
of n

9. Summary
•The general term lets you find any term in a linear
sequence
•It's written as:
an=a+(n−1)d
•Practice helps build speed and accuracy!