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4PM1/02 Jun 2020, Question 5: Sigma Notation

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks

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The question, in short

Prove the given summation formula for 3r + 5, use it to evaluate a related sum, and solve for n when the total equals 385.

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

Part (a) · 3 marks

Show that the sum from r = 1 to n of (3r + 5) equals (1/2)n(3n + 13).

  1. 1The terms are 8, 11, 14, …, (3n + 5): arithmetic with a = 8, last term 3n + 5
  2. 2Sum = (n/2)(first + last) = (n/2)(8 + 3n + 5)
  3. 3= (1/2)n(3n + 13)

AnswerΣ (3r + 5) = (1/2)n(3n + 13) shown

Part (b) · 2 marks

Using part a, evaluate the sum from r = 35 to 50 of (3r + 5).

  1. 1Σ from 35 to 50 = Σ from 1 to 50 − Σ from 1 to 34
  2. 2= (50/2)(13 + 150) − (34/2)(13 + 102)
  3. 3= 4075 − 1955 = 2120

Answer2120

Part (c) · 3 marks

Given the sum from r = 1 to n of (3r + 5) = 385, find n.

  1. 1(n/2)(13 + 3n) = 385
  2. 23n² + 13n − 770 = 0
  3. 3(3n + 55)(n − 14) = 0
  4. 4n = 14

Answern = 14

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