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Date	May 2018	Marks available	2	Reference code	18M.2.sl.TZ2.4
Level	SL only	Paper	2	Time zone	TZ2
Command term	Find	Question number	4	Adapted from	N/A

Question

The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200.

Find the common ratio.

[2]

Find the sum of the first 8 terms.

[2]

Find the least value of n for which S_n > 163.

[3]

Markscheme

correct substitution into infinite sum (A1)
eg \(200 = \frac{4}{{1 - r}}\)

r = 0.98 (exact) A1 N2

[2 marks]

correct substitution (A1)

\(\frac{{4\left( {1 - {{0.98}^8}} \right)}}{{1 - 0.98}}\)

29.8473

29.8 A1 N2

[2 marks]

attempt to set up inequality (accept equation) (M1)
eg \(\frac{{4\left( {1 - {{0.98}^n}} \right)}}{{1 - 0.98}} > 163,\,\,\frac{{4\left( {1 - {{0.98}^n}} \right)}}{{1 - 0.98}} = 163\)

correct inequality for n (accept equation) or crossover values (A1)
eg n > 83.5234, n = 83.5234, S₈₃ = 162.606 and S₈₄ = 163.354

n = 84 A1 N1

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1 - Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.

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