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Date	May 2017	Marks available	2	Reference code	17M.1.SL.TZ2.T_9
Level	Standard Level	Paper	Paper 1 (with calculator from previous syllabus)	Time zone	Time zone 2
Command term	Find	Question number	T_9	Adapted from	N/A

Question

Consider the geometric sequence ${u_1} = 18,{\text{ }}{u_2} = 9,{\text{ }}{u_3} = 4.5,{\text{ }} \ldots$ .

Write down the common ratio of the sequence.

[1]

Find the value of ${u_5}$ .

[2]

Find the smallest value of $n$ for which ${u_n}$ is less than ${10^{ - 3}}$ .

[3]

Markscheme

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

$\frac{1}{2}{\text{ }}(0.5)$ (A1) (C1)

[1 mark]

$18 \times {\left( {\frac{1}{2}} \right)^4}$ (M1)

Note: Award (M1) for their correct substitution into the geometric sequence formula. Accept a list of their five correct terms.

$1.125{\text{ }}\left( {1.13,{\text{ }}\frac{9}{8}} \right)$ (A1)(ft) (C2)

Note: Follow through from their common ratio from part (a).

[2 marks]

$18 \times {\left( {\frac{1}{2}} \right)^{n - 1}} < {10^{ - 3}}$ (M1)(M1)

Notes: Award (M1) for their correct substitution into the geometric sequence formula with a variable in the exponent, (M1) for comparing their expression with ${10^{ - 3}}{\text{ }}\left( {\frac{1}{{1000}}} \right)$ .

Accept an equation.

$n = 16$ (A1)(ft) (C3)

Note: Follow through from their common ratio from part (a). “ $n$ ” must be a positive integer for the (A1) to be awarded.

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.3—Geometric sequences and series

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