Extrapolating linear, quadratic, and exponential patterns

Extend linear, quadratic, and exponential sequences term by term using constant first differences, constant second differences, or constant ratios.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-7
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y9-11

Resources

Terminology

  • pattern
  • linear pattern
  • quadratic pattern
  • exponential pattern
  • constant difference
  • first differences
  • second differences
  • constant ratio
  • sequence
  • term
  • extend
  • extrapolate

Task goals

  • Extend linear patterns using constant differences.
  • Predict terms in quadratic patterns using differences and second differences.
  • Continue exponential patterns by identifying the constant multiplier.
  • Extrapolate several places beyond the given terms while recording the repeated difference or ratio.

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Extrapolating linear, quadratic, and exponential patterns

Extrapolating linear, quadratic, and exponential patterns

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