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WMA12/01 Jun 2024, Question 2: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Arithmetic series with sixth term 2 and sum of first ten terms −80; find the first term and common difference, then the least n with Sₙ > 8000.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Find the first term and the common difference of the arithmetic series.

  1. 1Sixth term: a + 5d = 2
  2. 2Sum of ten terms: (10/2)(2a + 9d) = −80, so 2a + 9d = −16
  3. 3Double the first: 2a + 10d = 4; subtract: d = 20
  4. 4a = 2 − 5(20) = −98

Answera = −98, d = 20

Part (b) · 3 marks

Using your values, find the smallest n for which the sum Sₙ exceeds 8000.

  1. 1(n/2)(2(−98) + (n − 1)20) > 8000
  2. 2n(−196 + 20n − 20) > 16000, so 20n² − 216n − 16000 > 0
  3. 35n² − 54n − 4000 > 0
  4. 4Positive root: n = (54 + √(54² + 80000))/10 ≈ 34.2
  5. 5Smallest integer n = 35

Answern = 35

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Also searched as: WMA12 June 2024 · WMA12/01 · wma12 jun24 · IAS Maths Pure Mathematics 2 June 2024 · question 2.
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