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A-LevelMathematicsSeries9709/12 · Oct/Nov 2018 · Q57 Marks

The first three terms of an arithmetic progression are 4, x and y respectively. The first three terms of a geometric progression are x, y and 18 respectively. It is given that both x and y are positive.

  1. (i)Find the value of x and the value of y.[4]
  2. (ii)Find the fourth term of each progression.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [B1] From the AP: x - 4 = y - x
  2. [B1] From the GP: y/x = 18/y
  3. [M1] Simultaneous equations: y² - 9y - 36 = 0 or 2x² - 17x + 8 = 0
  4. [A1] x = 8, y = 12.
  5. [B1] AP 4th term = 16
  6. [M1] GP 4th term = 8 × (12/8)³
  7. [A1] = 27

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About this question

Topic
Series, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2018 Paper 1 Variant 2, question 5.

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