| 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 \({u_1}\).
(i) Given that \({u_n} = 516\) , find the value of n .
(ii) For this value of n , find \({S_n}\) .
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]
(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]
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.
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.
