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Date May 2019 Marks available 2 Reference code 19M.2.SL.TZ1.S_7
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number S_7 Adapted from N/A

Question

The first terms of an infinite geometric sequence, un, are 2, 6, 18, 54, …

The first terms of a second infinite geometric sequence, vn, are 2, −6, 18, −54, …

The terms of a third sequence, wn, are defined as wn=un+vn.

The finite series, 225k=1wk , can also be written in the form mk=04rk.

Write down the first three non-zero terms of wn.

[3]
a.

Find the value of r.

[2]
b.i.

Find the value of m.

[2]
b.ii.

Markscheme

attempt to add corresponding terms      (M1)

eg   2+2,6+(6),2(3)n1+2(3)n1

correct value for w5        (A1)

eg   324

4, 36, 324 (accept 4 + 36 + 324)      A1 N3

[3 marks]

a.

valid approach     (M1)

eg  4×r1=36,  4×9n1

r=9  (accept mk=04×9km may be incorrect)      A1 N2

[2 marks]

b.i.

recognition that 225 terms of wn consists of 113 non-zero terms    (M1)

eg  11311120,  113

m=112  (accept 1k=0124×rkr may be incorrect)      A1 N2

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 1—Number and algebra » SL 1.2—Arithmetic sequences and series
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Topic 1—Number and algebra

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