AQA · Mathematics · 8300
GCSE Maths: Iterative Processes
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths video for Iterative Processes (Corbettmaths Video 373), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does the iterative formula P(n+1) = 1.02 × P(n) mean?
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Each year's value is found by multiplying the previous year's value by 1.02 (a 2% increase each year).
If P(1) = 80 000 and P(n+1) = 1.02 × P(n), what is P(2)?
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81 600 (1.02 × 80 000).
If P(1) = 80 000 and P(n+1) = 1.02 × P(n), what is P(3)?
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83 232 (1.02 × 81 600).
Which calculator button makes repeating an iterative formula quick?
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The ANS button — type the formula using ANS, then press = repeatedly to get each successive term.
If T(1) = 1000 and T(n+1) = 0.9 × T(n) + 200, what is T(2)?
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1100 (0.9 × 1000 + 200).
If T(1) = 1000 and T(n+1) = 0.9 × T(n) + 200, what is T(4)?
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1271 (T(2) = 1100, T(3) = 1190, T(4) = 0.9 × 1190 + 200 = 1271).
In M(t+1) = k × M(t), how do you find the constant k from two consecutive values?
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Divide the later value by the earlier one: k = M(t+1) ÷ M(t).
A mass decays from 200 kg to 176 kg in one year via M(t+1) = k × M(t). What is k?
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k = 176 ÷ 200 = 0.88.
A constant multiplier of 0.88 in an iterative formula means the quantity decreases by ?% each step.
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12
Why can the ANS button be used for iterative formulae with an added constant, e.g. 0.9 × ANS + 200?
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Because ANS always holds the previous term, so the whole formula (including the + 200) is re-applied each time you press =.
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