O-LevelAdditional MathematicsSeries4037/11 · May/June 2025 · Q119 Marks

An arithmetic progression has common difference d. The 3rd term of this progression is 10.

(a)Write down expressions for the 1st term and the 2nd term of this progression. Give your answers in terms of d only.[2]
(b)When each of the first 3 terms is squared, the sum of these squares is 140 . There are two possible values for d. Using your answer to part (a), find the sum of the first 200 terms of the progression with the smaller value of d.[7]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B2] 10-2d and 10-d
[M1] FT from their two terms in (a), must be both 2 terms expression in terms of d only or Correct expressions in terms of a only, must see substitution and expansion
[A1] Correct equation in solvable form 5d²-60d+160=0 oe
[M1] Factorises their 3-term quadratic expression or solves their 3-term quadratic equation
[A1] d=8 d=4
[M1] FT 10-2(their d); Finds the first term when d = 4: a = 2
[M1] FT their a and their d; [S200 =] 200/2 {4+199×4} oe
[A1] 80 000

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About this question

Topic

Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.

Source

O-Level Additional Mathematics, May/June 2025 Paper 1 Variant 1, question 11.

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