O-LevelAdditional MathematicsSeries4037/12 · Oct/Nov 2022 · Q108 Marks

The first three terms of an arithmetic progression are lgx, lgx³, lgx⁹, where x > 0.

(a)Show that the sum to n terms of this arithmetic progression can be written as n(pn-1)lgx, where p is an integer.[4]
(b)Hence find the value of n for which the sum to n terms is equal to 4950lgx.[2]
(c)Given that this sum to n terms is also equal to -14850, find the exact value of x.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[1] (a) Common difference = 4lgx
[1] (a) For use of the sum formula S_n = n/2 (2a + (n-1)d) with their common difference
[1] (a) For a correct attempt to rearrange to the required form n(2n-1)lgx
[1] (a) Final answer n(2n-1)lgx shown correctly (AG)
[1] (b) For n((their p)n-1)=4950 together with an attempt to solve to obtain n
[1] (b) n = 50 (cao)
[1] (c) For use of their n and p in a complete method to find x or use of part (b)
[1] (c) x = 10⁻³ or equivalent

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Topic: Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2022 Paper 1 Variant 2, question 10.

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