Sequences - problem solving strategies

• Carefully read the problem.
• Decide what you are trying to do.
• Identify the relevant information.
• Restate the problem.
• Make comparisons with a related problem.
• Look at simple cases.
• Be systematic.
• Draw a picture.
• Use materials eg. squared paper, counters, cubes, coloured pencils
• Make a list.
• Make a table.
• Draw a graph.
• Look for a pattern.
• Describe the pattern.
• Check the pattern.
• Use algebraic language (formula for the general term of a sequence, ...).
• Explain the pattern (justification or proof of the formula for the general term of a sequence, ...).
• Summarise your results.
• Suggest extensions to the problem.

How do people solve problems?

Mary O'Mears, creative director at Young & Rubicam in the 1960's, gave an answer to that question.

In order to justify or prove the formula for the general term of a sequence, there are three main types of mathematical proof:

• direct or deductive proof
• proof by contradiction - example from Dr Math
• proof by mathematical induction - activity.