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Date	May 2017	Marks available	3	Reference code	17M.1.SL.TZ1.S_7
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 1
Command term	Find	Question number	S_7	Adapted from	N/A

Question

The first three terms of a geometric sequence are $\ln {x^{16}}$ , $\ln {x^8}$ , $\ln {x^4}$ , for $x > 0$ .

Find the common ratio.

Markscheme

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

correct use $\log {x^n} = n\log x$ A1

eg $\,\,\,\,\,$ $16\ln x$

valid approach to find $r$ (M1)

eg $\,\,\,\,\,$ $\frac{{{u_{n + 1}}}}{{{u_n}}},{\text{ }}\frac{{\ln {x^8}}}{{\ln {x^{16}}}},{\text{ }}\frac{{4\ln x}}{{8\ln x}},{\text{ }}\ln {x^4} = \ln {x^{16}} \times {r^2}$

$r = \frac{1}{2}$ A1 N2

[3 marks]

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Syllabus sections

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

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