| Date | November 2008 | Marks available | 5 | Reference code | 08N.2.hl.TZ0.2 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
A geometric sequence has a first term of 2 and a common ratio of 1.05. Find the value of the smallest term which is greater than 500.
Markscheme
\(2 \times {1.05^{n - 1}} > 500\) M1
\(n - 1 > \frac{{\log {\text{ }}250}}{{\log {\text{ }}1.05}}\) M1
\(n - 1 > 113.1675…\) A1
\(n = 115\) (A1)
\({u_{115}} = 521\) A1 N5
Note: Accept graphical solution with appropriate sketch.
[5 marks]
Examiners report
Many candidates misread the question and stopped at showing that the required term was the \({115^{{\text{th}}}}\).
Syllabus sections
Topic 1 - Core: Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.
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