O-LevelAdditional MathematicsSeries4037/21 · May/June 2021 · Q1110 Marks

The 2nd, 8th and 44th terms of an arithmetic progression form the first three terms of a geometric progression. In the arithmetic progression, the first term is 1 and the common difference is positive.

(a)(i)Show that the common difference of the arithmetic progression is 5.[5]
(a)(ii)Find the sum of the first 20 terms of the arithmetic progression.[2]
(b)(i)Find the 5th term of the geometric progression.[2]
(b)(ii)Explain whether or not the sum to infinity of this geometric progression exists.[1]

Mark scheme

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

[B1] 1+d, 1+7d, 1+43d soi
[M2] (1+7d)² = (1+d)(1+43d) oe
[A1] 6d²-30d=0 oe nfww
[A1] Verifies that d = 5 by substitution or factorises and solves to obtain d = 5 only
[M1] S20 = 20/2 * {2[1]+(20-1)(5)}
[A1] 970
[B2] 7776 nfww
[B1] for 6 × 6^(5-1)
[B1] Valid explanation e.g. The sum to infinity does not exist for this GP as the common ratio is greater than 1.

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Topic: Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source: O-Level Additional Mathematics, May/June 2021 Paper 2 Variant 1, question 11.

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