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Date May 2017 Marks available 6 Reference code 17M.2.SL.TZ2.S_5
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number S_5 Adapted from N/A

Question

Consider a geometric sequence where the first term is 768 and the second term is 576.

Find the least value of n such that the nth term of the sequence is less than 7.

Markscheme

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

attempt to find r     (M1)

eg576768, 768576, 0.75

correct expression for un     (A1)

eg768(0.75)n1

EITHER (solving inequality)

valid approach (accept equation)     (M1)

egun<7

valid approach to find n     M1

eg768(0.75)n1=7, n1>log0.75(7768), sketch

correct value

egn=17.3301     (A1)

n=18 (must be an integer)     A1     N2

OR (table of values)

valid approach     (M1)

egun>7, one correct crossover value

both crossover values, u17=7.69735 and u18=5.77301     A2

n=18 (must be an integer)     A1     N2

OR (sketch of functions)

valid approach     M1

egsketch of appropriate functions

valid approach     (M1) 

egfinding intersections or roots (depending on function sketched)

correct value

egn=17.3301     (A1)

n=18 (must be an integer)     A1     N2

[6 marks]

Examiners report

[N/A]

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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