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Achievement objective M7-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • use arithmetic and geometric sequences and series.


  • Identifies and uses representations such as geometric patterns, coordinates, lists of terms, recursive formulae, general formulae, and sigma notation.
  • Solves problems that can be modelled by arithmetic and geometric sequences and series.
  • Makes links with algebraic manipulation M7-6, solving equations M7-7, and simultaneous equations M7-8.
  • See key mathematical ideas on NZmaths.


M7-3 links from NA6-1, NA6-3, GM6-1, and to M8-3.

Possible context elaborations

  • Biological applications such as rate of infection and population growth.
  • Radioactive decay, temperature drop, (for example, as applied in forensic evidence).
  • Financial applications such as inflation/depreciation, interest on savings.
  • Physical applications such as bouncing ball, swinging pendulum, bungee jumping.
  • Bouncing balls: Finding the total distance a ball bounces.
  • Car depreciation
  • Dear Aunt Lucy
  • Interesting curves: Exploring perimeter and area of curves.
  • Investments and loans
  • Mortgage payments: Investigating the difference between paying fortnightly and monthly load repayments.
  • Population explosion: Exploring population growth with different scenarios.
  • Powhiri investigation: Exploring the number of ancestors.
  • Saving to study: Exploring savings rates.
  • Skyscraper: Skyscraper rental rates.
  • Tax it! Exploring a fictional taxation system on gambling profits.
  • Word of mouth: How many people find out about a business using word of mouth?
  • Investigate half-lives of various radioactive substances. Investigate the application of a sequence in carbon dating. Which type of sequence best models radioactive decay? Can an equation be written?
  • Falling birth rate: The birth rate in a country is falling by 5% every year. In 2001 there were 65,000 births. How many babies were born the following year? Two years later? Five years later?

Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO:

Last updated September 10, 2018