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Date	May 2017	Marks available	4	Reference code	17M.1.AHL.TZ2.H_3
Level	Additional Higher Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 2
Command term	Find	Question number	H_3	Adapted from	N/A

Question

The 1st, 4th and 8th terms of an arithmetic sequence, with common difference $d$ , $d \ne 0$ , are the first three terms of a geometric sequence, with common ratio $r$ . Given that the 1st term of both sequences is 9 find

the value of $d$ ;

[4]

the value of $r$ ;

[1]

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

EITHER

the first three terms of the geometric sequence are $9$ , $9r$ and $9{r^2}$ (M1)

$9 + 3d = 9r( \Rightarrow 3 + d = 3r)$ and $9 + 7d = 9{r^2}$ (A1)

attempt to solve simultaneously (M1)

$9 + 7d = 9{\left( {\frac{{3 + d}}{3}} \right)^2}$

the ${{\text{1}}^{{\text{st}}}}$ , ${{\text{4}}^{{\text{th}}}}$ and ${{\text{8}}^{{\text{th}}}}$ terms of the arithmetic sequence are

$9,{\text{ }}9 + 3d,{\text{ }}9 + 7d$ (M1)

$\frac{{9 + 7d}}{{9 + 3d}} = \frac{{9 + 3d}}{9}$ (A1)

attempt to solve (M1)

THEN

$d = 1$ A1

[4 marks]

$r = \frac{4}{3}$ A1

Note: Accept answers where a candidate obtains $d$ by finding $r$ first. The first two marks in either method for part (a) are awarded for the same ideas and the third mark is awarded for attempting to solve an equation in $r$ .

[1 mark]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.2—Arithmetic sequences and series

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