O-LevelAdditional MathematicsSeries4037/22 · Oct/Nov 2021 · Q1010 Marks

The first three terms of an arithmetic progression are x, 5x-4 and 8x +2. Find x and the common difference.

(a)The first three terms of an arithmetic progression are x, 5x-4 and 8x +2. Find x and the common difference.[4]
(b)(i)The first three terms of a geometric progression are y, 5y -4 and 8y+2. Find the two possible values of y.[4]
(b)(ii)For each of these values of y, find the corresponding value of the common ratio.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[M2] B1 for one correct equation seen, e.g. d = 4x-4 oe or d = 3x+6 oe or 2d = 7x+2 oe May come from the sum of terms, e.g. 11x – 3d = 2 Eliminate one unknown using two correct equations e.g. d = 4x-4 oe d = 3x+6 oe and solve as far as x = ... or d=...
[A1] x=10
[A1] d=36
[M1] (5y-4)/y = (8y+2)/(5y-4) oe
[M1] 25y² - 40y+16=8y² + 2y
[M1] Solves their 3-term quadratic -> 17y² - 42y+16[= 0]
[A1] Both values (17y-8)(y-2)[=0] 8/17, 2
[B2] B1 for one correct 7/2, 3

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Topic: Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2021 Paper 2 Variant 2, question 10.

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