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Sequences and series in modellingEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

  • When is an arithmetic model appropriate?
  • When is a geometric model appropriate?
  • What multiplier represents a 6\% increase? A 6\% decrease?
  • How do you find the first term to exceed a target in an arithmetic model?
  • How do you find the first term to exceed a target in a geometric model?
  • Total saved after n months, saving a then d more each month?
  • Total saved after n years, depositing P at the start of each year at rate r (multiplier)?
  • Why does a geometric growth model with |r|<1 have a maximum?
  • What is the maximum height if the starting height is h0 and growths form a series with first term a and ratio r (|r|<1)?
  • Why must an answer to 'in which month...' be a whole number?
  • Give one limitation of a compound-interest model over 10 years.
  • What does b{n+1}=1.01bn-200 model?

Exam questions on Sequences and series in modelling

  1. Aisha saves money each month. In month 1 she saves £50, and in each later month she saves £8 more than in the previous month.
    Find the first month in which Aisha saves more than £300.2 marks
  2. A tree is 1.20 m tall when planted. It grows 0.50 m in the first year, and in each later year its growth is 85% of its growth in the previous year.
    Find the height of the tree after 5 years.2 marks
  3. At the start of each year Ben pays £1500 into a savings account that pays 3% compound interest, added at the end of each year. The first payment is at the start of year 1 and no money is withdrawn.
    Show that the amount in the account at the end of year 3 is £4775.44.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).