4PM1/02R Jun 2020, Question 1: Geometric Progressions and Sum to Infinity
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks
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The question, in short
Arithmetic series A has terms aₙ and geometric series G has terms tₙ, with a₁ = t₁, a₁₀ = t₃ = 48 and a₁₀ = 4t₂. Find the common ratio of G and the common difference of A.
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Solution · 6 marks
- 1Let a = a₁ = t₁: ar² = a + 9d = 48 and a + 9d = 4ar
- 2So ar² = 4ar
- 34ar/ar² = 1 ⇒ 4/r = 1 ⇒ r = 4
- 4a × 16 = 48 ⇒ a = 3
- 53 + 9d = 48 ⇒ d = 5
Answer(i) r = 4 (ii) d = 5
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