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O-LevelAdditional MathematicsSeries4037/21 · May/June 2025 · Q118 Marks

A geometric progression has first term a and common ratio r, where r > 0. The sum of the 2nd and 3rd terms of the progression is 168. The sum of the 4th and 5th terms of the progression is 94.5.

  1. (a)Find the 6th term of the progression.[7]
  2. (b)Find the sum to infinity of the progression.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

  1. [B1] ar + ar² = 168 or ar³ + ar⁴ = 94.5 oe soi
  2. [M1] Correct equation where a can be directly eliminated ar³(1+r) / ar(1+r) = 94.5 / 168 oe
  3. [M1] 168r² = 94.5 oe
  4. [A1] r = 3/4 only nfww
  5. [M1] FT their r -a - a(3/4) = 168 oe
  6. [A1] a = 128
  7. [B1] u₆ = 243/8 only oe, isw
  8. [B1] 512

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2025 Paper 2 Variant 1, question 11.

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