| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.sl.TZ1.10 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 10 | Adapted from | N/A |
Question
The first three terms of a geometric sequence are \({u_1} = 486,{\text{ }}{u_2} = 162,{\text{ }}{u_3} = 54\).
Find the value of \(r\), the common ratio of the sequence.
Find the value of \(n\) for which \({u_n} = 2\).
Find the sum of the first 30 terms of the sequence.
Markscheme
\(\frac{{162}}{{486}}\)\(\,\,\,\)OR\(\,\,\,\)\(\frac{{54}}{{162}}\) (M1)
Note: Award (M1) for dividing any \({u_{n + 1}}\) by \({u_n}\).
\( = \frac{1}{3}{\text{ }}(0.333,{\text{ }}0.333333 \ldots )\) (A1) (C2)
[2 marks]
\(486{\left( {\frac{1}{3}} \right)^{n - 1}} = 2\) (M1)
Note: Award (M1) for their correct substitution into geometric sequence formula.
\(n = 6\) (A1)(ft) (C2)
Note: Follow through from part (a).
Award (A1)(A0) for \({u_6} = 2\) or \({u_6}\) with or without working.
[2 marks]
\({S_{30}} = \frac{{486\left( {1 - {{\frac{1}{3}}^{30}}} \right)}}{{1 - \frac{1}{3}}}\) (M1)
Note: Award (M1) for correct substitution into geometric series formula.
\( = 729\) (A1)(ft) (C2)
[2 marks]
