| Date | May 2013 | Marks available | 2 | Reference code | 13M.2.sl.TZ1.1 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
An arithmetic sequence is given by \(5\), \(8\), \(11\), ….
(a) Write down the value of \(d\) .
(b) Find
(i) \({u_{100}}\) ;
(ii) \({S_{100}}\) .
(c) Given that \({u_n} = 1502\) , find the value of \(n\) .
Write down the value of \(d\) .
Find
(i) \({u_{100}}\) ;
(ii) \({S_{100}}\) .
Given that \({u_n} = 1502\) , find the value of \(n\) .
Markscheme
(a) \(d = 3\) A1 N1
[1 mark]
(b) (i) correct substitution into term formula (A1)
e.g. \({u_{100}} = 5 + 3(99)\) , \(5 + 3(100 - 1)\)
\({u_{100}} = 302\) A1 N2
(ii) correct substitution into sum formula (A1)
eg \({S_{100}} = \frac{{100}}{2}(2(5) + 99(3))\) , \({S_{100}} = \frac{{100}}{2}(5 + 302)\)
\({S_{100}} = 15350\) A1 N2
[4 marks]
(c) correct substitution into term formula (A1)
eg \(1502 = 5 + 3(n - 1)\) , \(1502 = 3n + 2\)
\(n = 500\) A1 N2
[2 marks]
Total [7 marks]
\(d = 3\) A1 N1
[1 mark]
(i) correct substitution into term formula (A1)
e.g. \({u_{100}} = 5 + 3(99)\) , \(5 + 3(100 - 1)\)
\({u_{100}} = 302\) A1 N2
(ii) correct substitution into sum formula (A1)
eg \({S_{100}} = \frac{{100}}{2}(2(5) + 99(3))\) , \({S_{100}} = \frac{{100}}{2}(5 + 302)\)
\({S_{100}} = 15350\) A1 N2
[4 marks]
correct substitution into term formula (A1)
eg \(1502 = 5 + 3(n - 1)\) , \(1502 = 3n + 2\)
\(n = 500\) A1 N2
[2 marks]
Total [7 marks]
Examiners report
The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.
The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.
The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.
The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.
