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Date November 2019 Marks available 2 Reference code 19N.1.SL.TZ0.T_7
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number T_7 Adapted from N/A

Question

A geometric sequence has a first term of 83 and a fourth term of 9.

Find the common ratio.

[2]
a.

Write down the second term of this sequence.

[1]
b.

The sum of the first k terms is greater than 2500.

Find the smallest possible value of k.

[3]
c.

Markscheme

9=(83)r3      (M1)

Note: Award (M1) for correctly substituted geometric sequence formula equated to 9.

(r=)1.5(32)         (A1) (C2)

[2 marks]

a.

4         (A1)(ft)  (C1)

Note: Follow through from part (a).

[1 mark]

b.

2500<(83)((1.5)k1)1.51       (M1)

Note: Award (M1) for their correctly substituted geometric series formula compared to 2500.

k=15.2(15.17319)        (A1)(ft)

(k=)16        (A1)(ft)    (C3)

Note: Answer must be an integer for the final (A1)(ft) to be awarded.
Follow through from part (a).

[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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