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Date May 2014 Marks available 3 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]
a.

Find the first term.

[2]
b.

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

[3]
c.

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]

a.

correct approach     (A1)

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

\({u_1} = 4\)     A1     N2

[2 marks]

b.

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]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

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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