Paper 1 · Sequences and Series ⏱ Tested in 2 exam questions since 2022 Lesson 12 of 15

Sequences and series 9: Geometric Sequences 5

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You’ll learn

  • Write a recurring decimal as a fraction by summing its geometric series with S∞
  • Identify a and r from the recurring block (r = 1/10ⁿ for an n-digit block)
  • Handle non-recurring prefixes and leading zeros (2.2̇5̇ = 223/99, 0.01̇5̇ = 1/66)
  • Explain why every recurring decimal is a rational number

Most recent exam questions

  • 2025 Paper 1 Q7(b)(ii) — sum of a geometric series — page-22 formula Sₙ = a(rⁿ − 1)/(r − 1)
  • 2022 Paper 1 Q9(e) — sum to infinity of a convergent geometric series

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