| Date | May 2008 | Marks available | 2 | Reference code | 08M.2.sl.TZ2.1 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Consider the infinite geometric sequence \(3000{\text{, }}- 1800{\text{, }}1080{\text{, }} - 648, \ldots \) .
Find the common ratio.
Find the 10th term.
Find the exact sum of the infinite sequence.
Markscheme
evidence of dividing two terms (M1)
e.g. \( - \frac{{1800}}{{3000}}\) , \( - \frac{{1800}}{{1080}}\)
\(r = - 0.6\) A1 N2
[2 marks]
evidence of substituting into the formula for the 10th term (M1)
e.g. \({u_{10}} = 3000{( - 0.6)^9}\)
\({u_{10}} = 30.2\) (accept the exact value \( - 30.233088\)) A1 N2
[2 marks]
evidence of substituting into the formula for the infinite sum (M1)
e.g. \(S = \frac{{3000}}{{1.6}}\)
\(S = 1875\) A1 N2
[2 marks]
Examiners report
This question was generally well done by most candidates.
This question was generally well done by most candidates, although quite a few showed difficulty answering part (b) exactly or to three significant figures.
This question was generally well done by most candidates, although quite a few showed difficulty answering part (b) exactly or to three significant figures. Some candidates reversed the division of terms to obtain a ratio of \( - \frac{5}{3}\). Of these, most did not recognize this ratio as an inappropriate value when finding the sum in part (c).
