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WMA12/01 Oct 2023, Question 2: Sequences: Formulas and Recurrence

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 5 marks

The question, in short

A sequence has u₁ = 3 and uₙ₊₁ = 2 − 4/uₙ. Find early terms and then the sum of the first 100 terms.

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

Part (a) · 3 marks

Use the recurrence with u₁ = 3 to calculate u₂, u₃ and u₄.

  1. 1u₂ = 2 − 4/3 = 2/3
  2. 2u₃ = 2 − 4 ÷ (2/3) = 2 − 6 = −4
  3. 3u₄ = 2 − 4/(−4) = 2 + 1 = 3

Answeru₂ = 2/3, u₃ = −4, u₄ = 3

Part (b) · 2 marks

Find the sum from r = 1 to 100 of uᵣ.

  1. 1The sequence repeats every 3 terms: 3, 2/3, −4, 3, …
  2. 2Sum of one cycle = 3 + 2/3 − 4 = −1/3
  3. 3100 terms = 33 full cycles + 1 extra term (u₁₀₀ = 3)
  4. 4Sum = 33 × (−1/3) + 3 = −11 + 3 = −8

Answer−8

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Also searched as: WMA12 October 2023 · WMA12/01 · wma12 oct23 · IAS Maths Pure Mathematics 2 October 2023 · question 2.
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