PROBLEM SOLVING

Sequences

Learn the reliable method for sequences, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Algebra uses letters to represent numbers and relationships.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Translate the rule or wording into an expression.
  2. Substitute known values carefully, using brackets for negative values.
  3. Simplify in the correct order and check the result against the original relationship.
3 · WORKED EXAMPLES

See the method in action

Example 1

The pattern continues in the same way. How many sticks are in term 5?

Term 1
Term 2
Term 3
  1. Each new square adds 4 sticks.
  2. Term t therefore contains 4t sticks.
  3. For term 5, 4 × 5 + 0 = 20.
Answer: 20
Example 2

The pattern continues in the same way. How many sticks are in term 13?

Term 1
Term 2
Term 3
  1. Each new square adds 3 sticks, because one edge is shared.
  2. Term t therefore contains 3t + 1 sticks.
  3. For term 13, 3 × 13 + 1 = 40.
Answer: 40
4 · ELEVENSPRINT TIP

A useful shortcut

Simplify in the correct order and check the result against the original relationship.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.