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Date May 2012 Marks available 3 Reference code 12M.2.sl.TZ1.1
Level SL only Paper 2 Time zone TZ1
Command term Find and Write down Question number 1 Adapted from N/A

Question

The first three terms of an arithmetic sequence are 36, 40, 44,….

(i)     Write down the value of d .

(ii)    Find \({u_8}\) .

[3]
a(i) and (ii).

(i)     Show that \({S_n} = 2{n^2} + 34n\) .

(ii)    Hence, write down the value of \({S_{14}}\) .

[3]
b(i) and (ii).

Markscheme

(i) \(d = 4\)     A1     N1

(ii) evidence of valid approach     (M1)

e.g. \({u_8} = 36 + 7(4)\) , repeated addition of d from 36

\({u_8} = 64\)     A1     N2

[3 marks]

a(i) and (ii).

(i) correct substitution into sum formula     A1

e.g. \({S_n} = \frac{n}{2}\left\{ {2\left( {36} \right) + (n - 1)(4)} \right\}\) , \(\frac{n}{2}\left\{ {72 + 4n - 4} \right\}\)

evidence of simplifying

e.g. \(\frac{n}{2}\left\{ {4n + 68} \right\}\)     A1

\({S_n} = 2{n^2} + 34n\)     AG     N0

(ii) \(868\)     A1     N1

[3 marks]

b(i) and (ii).

Examiners report

The majority of candidates were successful with this question. Most had little difficulty with part (a).

a(i) and (ii).

Some candidates were unable to show the required result in part (b), often substituting values for n rather than working with the formula for the sum of an arithmetic series.

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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