Sequences

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Understanding Sequences & Patterns

A sequence is a list of numbers that follow a pattern. Being able to spot patterns and write rules for sequences is a key algebra skill tested in GCSE exams.

Key Points:

Arithmetic sequences have a constant difference between terms
The nth term rule lets you find ANY term without listing them all
To find the nth term: look at differences, then adjust
You can use the nth term to check if a number is in the sequence

Top Tips

  • Always find the difference between consecutive terms first
  • If the difference is 3, start your rule with 3n
  • Test your rule by substituting n=1, n=2 to check it works

Worked Examples

1Step 1: Find the common difference: 8-5=3, 11-8=3, 14-11=3
2Step 2: The difference is +3 each time
3Step 3: Next term: 14 + 3 = 17
4Step 4: Term after: 17 + 3 = 20
Answer: 17, 20

šŸŽ¬ Video Tutorials

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Sequences and Finding the nth Term

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Complete method for arithmetic sequences.

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Quadratic Sequences

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Finding the nth term of quadratic sequences.

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Rules to Follow

šŸ’” Click on any rule to see more details!

Common Difference

For arithmetic sequences, subtract consecutive ter...

nth Term Formula

nth term = dn + (a - d), where d = common differen...

Finding nth Term

Step 1: Find difference (d). Step 2: Write dn. Ste...

Special Sequences

Square: 1,4,9,16... (nĀ²). Triangular: 1,3,6,10... ...

Term vs Position

The 5th term means n=5. Substitute into the formul...