Compound Rules

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Sequences that combine multiple operations (like add then multiply) to generate each term.

Compound rule sequences apply more than one operation to get from one term to the next. Common combinations include 'multiply then add', 'add then multiply', or alternating between different operations. These sequences require recognizing that a single operation won't explain the pattern.

aₙ₊₁ = f(g(aₙ)), where f and g are different operations

• 2, 5, 11, 23, 47... (×2 then +1 each step)
• 1, 3, 7, 15, 31... (×2 then +1, or 2ⁿ - 1)
• 3, 7, 15, 31... (×2 + 1 each step)

How to recognize it

• Simple differences or ratios don't reveal a constant
• Try combinations: (term × k) + c or (term + c) × k
• Look for patterns like 'double and add one'
• The relationship between terms may need two operations

Common mistakes

• Assuming only one operation is involved
• Not trying different operation orders
• Missing that some compound rules simplify to formulas (like 2ⁿ - 1)

Practice guidance

Number Sequences