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4PM1/01 Jun 2023, Question 1: Sigma Notation

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks

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The question, in short

Prove the given summation formula for 3r + 2 from r = 1 to n, then use it to evaluate the sum of 3r + 2 from r = 10 to 40.

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

Part (a) · 3 marks

Show that the sum of 3r + 2 from r = 1 to n equals (n/2)(3n + 7).

  1. 1The terms 5, 8, 11, … form an arithmetic series with a = 5, d = 3
  2. 2Sum = (n/2)[2 × 5 + (n − 1) × 3]
  3. 3= (n/2)(10 + 3n − 3)
  4. 4= (n/2)(3n + 7)

AnswerΣ from r = 1 to n of (3r + 2) = (n/2)(3n + 7) shown

Part (b) · 2 marks

Using part a or another method, find the sum of 3r + 2 from r = 10 to 40.

  1. 1Sum from r = 10 to 40 = (sum to 40) − (sum to 9)
  2. 2Sum to 40 = 20(127) = 2540
  3. 3Sum to 9 = (9/2)(34) = 153
  4. 42540 − 153 = 2387

Answer2387

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