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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 ,   u 2 = 9 ,   u 3 = 4.5 ,   .

Write down the common ratio of the sequence.

[1]
a.

Find the value of u 5 .

[2]
b.

Find the smallest value of n for which u n is less than 10 3 .

[3]
c.

Markscheme

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

1 2   ( 0.5 )     (A1)     (C1)

[1 mark]

a.

18 × ( 1 2 ) 4     (M1)

 

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

 

1.125   ( 1.13 ,   9 8 )     (A1)(ft)     (C2)

 

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

 

[2 marks]

b.

18 × ( 1 2 ) 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   ( 1 1000 ) .

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]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

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

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