4PM1/01 Jun 2021, Question 4: Arithmetic Progressions in Problems
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks
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The question, in short
For the arithmetic series with nth term uₙ = (n + 1) ln 4, show the sum of the first n terms equals ln 2^(n² + an) and find the integer a.
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Solution · 5 marks
- 1u₁ = 2 ln 4, d = ln 4
- 2Sₙ = (n/2)(2 × 2 ln 4 + (n − 1) ln 4) = (n/2)(n + 3) ln 4
- 3ln 4 = 2 ln 2, so Sₙ = n(n + 3) ln 2
- 4Sₙ = (n² + 3n) ln 2 = ln 2^(n² + 3n), a = 3
AnswerSₙ = ln 2^(n² + 3n), so a = 3
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