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Date May 2018 Marks available 2 Reference code 18M.2.SL.TZ2.S_4
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number S_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]
a.

Find the sum of the first 8 terms.

[2]
b.

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

[3]
c.

Markscheme

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

correct substitution into infinite sum      (A1)
eg   200 = 4 1 r

= 0.98 (exact)     A1 N2

[2 marks]

a.

correct substitution     (A1)

4 ( 1 0.98 8 ) 1 0.98

29.8473

29.8    A1 N2

[2 marks]

b.

attempt to set up inequality (accept equation)      (M1)
eg   4 ( 1 0.98 n ) 1 0.98 > 163 , 4 ( 1 0.98 n ) 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]

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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