| Date | May 2009 | Marks available | 3 | Reference code | 09M.2.sl.TZ1.1 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
In an arithmetic series, the first term is –7 and the sum of the first 20 terms is 620.
Find the common difference.
Find the value of the 78th term.
Markscheme
attempt to substitute into sum formula for AP (accept term formula) (M1)
e.g. \({S_{20}} = \frac{{20}}{2}\left\{ {2( - 7) + 19\left. d \right\}} \right.\) , \(\left( {{\rm{or}}\frac{{20}}{2}\left( { - 7 + {u_{20}}} \right)} \right)\)
setting up correct equation using sum formula A1
e.g. \(\frac{{20}}{2}\left\{ {2( - 7) + \left. {19d} \right\}} \right. = 620\)
\(d = 4\) A1 N2
[3 marks]
correct substitution \({u_{78}} = - 7 + 77(4)\) (A1)
= 301 A1 N2
[2 marks]
Examiners report
This question was generally well answered. Many candidates who got part (a) wrong, recovered and received full follow through marks in part (b). There were a few candidates who confused the term and sum formula in part (a).
This question was generally well answered. Many candidates who got part (a) wrong, recovered and received full follow through marks in part (b). There were a few candidates who confused the term and sum formula in part (a).
