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Date May 2011 Marks available 3 Reference code 11M.2.sl.TZ1.3
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 3 Adapted from N/A

Question

In an arithmetic sequence \({u_1} = 7\) , \({u_{20}} = 64\) and \({u_n} = 3709\) .

Find the value of the common difference.

[3]
a.

Find the value of n .

[2]
b.

Markscheme

evidence of choosing the formula for 20th term     (M1)

e.g. \({u_{20}} = {u_1} + 19d\)

correct equation     A1

e.g. \(64 = 7 + 19d\) , \(d = \frac{{64 - 7}}{{19}}\)

\(d = 3\)     A1     N2

[3 marks]

a.

correct substitution into formula for \({u_n}\)     A1

e.g. \(3709 = 7 + 3(n - 1)\) , \(3709 = 3n + 4\)

\(n = 1235\)     A1     N1

[2 marks]

b.

Examiners report

The majority of candidates gained full marks in this question. However, the presentation of work was often disappointing, and there were a few incorrect trial and error approaches in part (a) resulting in division by 20 rather than 19.

a.

The majority of candidates gained full marks in this question. However, the presentation of work was often disappointing, and there were a few incorrect trial and error approaches in part (a) resulting in division by 20 rather than 19.

b.

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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