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Date May 2010 Marks available 2 Reference code 10M.2.sl.TZ1.2
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 2 Adapted from N/A

Question

Consider the arithmetic sequence 3, 9, 15, \(\ldots \) , 1353 .

Write down the common difference.

[1]
a.

Find the number of terms in the sequence.

[3]
b.

Find the sum of the sequence.

[2]
c.

Markscheme

common difference is 6     A1     N1

[1 mark]

a.

evidence of appropriate approach     (M1)

e.g. \({u_n} = 1353\)

correct working     A1

e.g. \(1353 = 3 + (n - 1)6\) , \(\frac{{1353 + 3}}{6}\)

\(n = 226\)     A1     N2

[3 marks]

b.

evidence of correct substitution     A1

e.g. \({S_{226}} = \frac{{226(3 + 1353)}}{2}\) , \(\frac{{226}}{2}(2 \times 3 + 225 \times 6)\)

\({S_{226}} = 153228\) (accept 153000)     A1     N1

[2 marks]

c.

Examiners report

Most candidates did well on this question. Any errors were usually arithmetic in nature but candidates were able to obtain follow-through marks on errors made in earlier parts.

a.

Most candidates did well on this question. Any errors were usually arithmetic in nature but candidates were able to obtain follow-through marks on errors made in earlier parts.

b.

Most candidates did well on this question. Any errors were usually arithmetic in nature but candidates were able to obtain follow-through marks on errors made in earlier parts.

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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