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WMA12/01 Jun 2019, Question 1: Sigma Notation

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 4 marks

The question, in short

A sequence is defined by aₙ₊₁ = 4 − aₙ with a₁ = 3. Find a₂, a₁₀₇, and the sum from n = 1 to 200 of (2aₙ − 1).

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

Part (ai) · 1 mark

Find the value of a₂ using the recurrence relation and a₁ = 3.

  1. 1a₂ = 4 − a₁ = 4 − 3
  2. 2a₂ = 1

Answera₂ = 1

Part (aii) · 1 mark

Find the value of a₁₀₇, using the pattern of the sequence.

  1. 1a₃ = 4 − 1 = 3, so the terms go 3, 1, 3, 1, ...
  2. 2Odd-numbered terms are 3 and 107 is odd
  3. 3a₁₀₇ = 3

Answera₁₀₇ = 3

Part (b) · 2 marks

Find the sum from n = 1 to 200 of (2aₙ − 1).

  1. 1For odd n: 2aₙ − 1 = 2(3) − 1 = 5
  2. 2For even n: 2aₙ − 1 = 2(1) − 1 = 1
  3. 3There are 100 odd and 100 even values of n from 1 to 200
  4. 4Sum = 100 × 5 + 100 × 1 = 600

Answer600

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Also searched as: WMA12 June 2019 · WMA12/01 · wma12 jun19 · IAS Maths Pure Mathematics 2 June 2019 · question 1.
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