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WMA12/01 Oct 2021, 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 = 6 and uₙ₊₁ = kuₙ + 3 with k positive. Find u₃ in terms of k, then use the sum of the first three terms equal to 117 to find k.

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

Part (a) · 2 marks

Use the recurrence with u₁ = 6 to write u₂ and then u₃, giving an expression in terms of k.

  1. 1u₂ = 6k + 3
  2. 2u₃ = k(6k + 3) + 3
  3. 3u₃ = 6k² + 3k + 3

Answeru₃ = 6k² + 3k + 3

Part (b) · 3 marks

Given that u₁ + u₂ + u₃ = 117, form an equation in k and solve for the positive value of k.

  1. 16 + (6k + 3) + (6k² + 3k + 3) = 117
  2. 26k² + 9k − 105 = 0
  3. 32k² + 3k − 35 = 0
  4. 4(2k − 7)(k + 5) = 0
  5. 5k is positive, so k = 7/2

Answerk = 7/2

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