Edexcel IALMathematicsGeneral Applications9 Marks
The first three terms of an arithmetic series are 2x, x+4, and 2x-5 respectively.
- (a)Show that x = 13.[3]
- (b)Find the common difference of the series.[2]
- (c)Find the sum of the first 20 terms of the series.[4]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for setting up the common difference equation: (x+4) - 2x = (2x-5) - (x+4).
- A1 for correctly expanding and simplifying to a linear equation in x, e.g., -x+4 = x-9.
- A1 for obtaining x = 13 (shown).
- M1 for substituting x=13 into two consecutive terms to find the common difference.
- A1 for common difference = (13+4) - 2(13) = 17 - 26 = -9.
- B1 for identifying the first term a = 2(13) = 26.
- M1 for using the sum of n terms formula Sₙ = n/2 [2a + (n-1)d] with n=20, their a and their d.
- A1 for S₂₀ = 20/2 [2(26) + (19)(-9)].
- A1 for S₂₀ = 10 [52 - 171] = 10 [-119] = -1190.
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