| Date | May 2012 | Marks available | 3 | Reference code | 12M.2.sl.TZ1.1 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Show that, Write down, and Hence | 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 \({u_8}\) .
(i) Show that \({S_n} = 2{n^2} + 34n\) .
(ii) Hence, write down the value of \({S_{14}}\) .
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]
(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]
Examiners report
The majority of candidates were successful with this question. Most had little difficulty with part (a).
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.
