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Date	May 2014	Marks available	2	Reference code	14M.1.sl.TZ1.2
Level	SL only	Paper	1	Time zone	TZ1
Command term	Find	Question number	2	Adapted from	N/A

Question

In an arithmetic sequence, the third term is 10 and the fifth term is 16.

Find the common difference.

[2]

Find the first term.

[2]

Find the sum of the first 20 terms of the sequence.

[3]

Markscheme

attempt to find $d$ (M1)

eg $\frac{{16 - 10}}{2}{\text{, }}10 - 2d = 16 - 4d{\text{, }}2d = 6{\text{, }}d = 6$

$d = 3$ A1 N2

[2 marks]

correct approach (A1)

eg $10 = {u_1} + 2 \times 3{\text{, }}10 - 3 - 3$

${u_1} = 4$ A1 N2

[2 marks]

correct substitution into sum or term formula (A1)

eg $\frac{{20}}{2}(2 \times 4 + 19 \times 3){\text{, }}{u_{20}} = 4 + 19 \times 3$

correct simplification (A1)

eg $8 + 57{\text{, }}4 + 61$

${S_{20}} = 650$ A1 N2

[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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