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Date May 2010 Marks available 4 Reference code 10M.2.sl.TZ2.2
Level SL only Paper 2 Time zone TZ2
Command term Find Question number 2 Adapted from N/A

Question

An arithmetic sequence, \({u_1}{\text{, }}{u_2}{\text{, }}{u_3} \ldots ,\) has \(d = 11\) and \({u_{27}} = 263\) .

Find \({u_1}\).

[2]
a.

(i)     Given that \({u_n} = 516\) , find the value of n .

(ii)    For this value of n , find \({S_n}\) .

[4]
b(i) and (ii).

Markscheme

evidence of equation for \({u_{27}}\)     M1

e.g. \(263 = {u_1} + 26 \times 11\) , \({u_{27}} = {u_1} + (n - 1) \times 11\) , \(263 - (11 \times 26)\)

\({u_1} = - 23\)     A1     N1

[2 marks]

a.

(i) correct equation     A1

e.g. \(516 = - 23 + (n - 1) \times 11\) , \(539 = (n - 1) \times 11\)

\(n = 50\)     A1     N1

(ii) correct substitution into sum formula     A1

e.g. \({S_{50}} = \frac{{50( - 23 + 516)}}{2}\) , \({S_{50}} = \frac{{50(2 \times ( - 23) + 49 \times 11)}}{2}\)

\({S_{50}} = 12325\) (accept 12300)     A1     N1

[4 marks]

b(i) and (ii).

Examiners report

This problem was done well by the vast majority of candidates. Most students set out their working very neatly and logically and gained full marks.

a.

This problem was done well by the vast majority of candidates. Most students set out their working very neatly and logically and gained full marks.

b(i) and (ii).

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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