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O-LevelAdditional MathematicsSeries4037/11 · May/June 2020 · Q912 Marks

An arithmetic progression has a second term of -14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.

  1. (a)An arithmetic progression has a second term of -14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.[5]
  2. (b)(i)A geometric progression has a second term of 27p² and a fifth term of p⁵. The common ratio, r, is such that 0 < r < 1. Find r in terms of p.[2]
  3. (b)(ii)Hence find, in terms of p, the sum to infinity of the progression.[3]
  4. (b)(iii)Given that the sum to infinity is 81, find the value of p.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [B1] Second term: a+d=-14
  2. [B1] Sum: 4=a+10d
  3. [B1] d=2
  4. [B1] a=-16
  5. [B1] Last term = 24 Ft on their d and their a
  6. [B1] For both equations
  7. [B1] r = p/3
  8. [M1] M1 for attempt to find a in terms of p
  9. [A1] a=81p
  10. [B1] Follow through on their a and their r
  11. [M1] For attempt to solve using their answer to (ii) as far as p = ...
  12. [A1] p = 3/4

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 12 marks.
Source
O-Level Additional Mathematics, May/June 2020 Paper 1 Variant 1, question 9.

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