| Date | November 2010 | Marks available | 2 | Reference code | 10N.1.sl.TZ0.1 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The first three terms of an infinite geometric sequence are 32, 16 and 8.
Write down the value of r .
Find \({u_6}\) .
Find the sum to infinity of this sequence.
Markscheme
\(r = \frac{{16}}{{32}}\left( { = \frac{1}{2}} \right)\) A1 N1
[1 mark]
correct calculation or listing terms (A1)
e.g. \(32 \times {\left( {\frac{1}{2}} \right)^{6 - 1}}\) , \(8 \times {\left( {\frac{1}{2}} \right)^3}\) , 32, \(\ldots \) 4, 2, 1
\({u_6} = 1\) A1 N2
[2 marks]
evidence of correct substitution in \({S_\infty }\) A1
e.g. \(\frac{{32}}{{1 - \frac{1}{2}}}\) , \(\frac{{32}}{{\frac{1}{2}}}\)
\({S_\infty } = 64\) A1 N1
[2 marks]
Examiners report
This question was very well done by the majority of candidates. There were some who used a value of r greater than one, with the most common error being \(r = 2\) .
This question was very well done by the majority of candidates. There were some who used a value of r greater than one, with the most common error being \(r = 2\) .
A handful of candidates struggled with the basic computation involved in part (c).
