| Date | May 2014 | Marks available | 4 | Reference code | 14M.1.sl.TZ2.7 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
The sums of the terms of a sequence follow the pattern
\({S_1} = 1 + k,{\text{ }}{S_2} = 5 + 3k,{\text{ }}{S_3} = 12 + 7k,{\text{ }}{S_4} = 22 + 15k,{\text{ }} \ldots ,{\text{ where }}k \in \mathbb{Z}.\)
Given that \({u_1} = 1 + k\), find \({u_2},{\text{ }}{u_3}\) and \({u_4}\).
Find a general expression for \({u_n}\).
Markscheme
valid method (M1)
eg \({u_2} = {S_2} - {S_1},{\text{ }}1 + k + {u_2} = 5 + 3k\)
\({u_2} = 4 + 2k,{\text{ }}{u_3} = 7 + 4k,{\text{ }}{u_4} = 10 + 8k\) A1A1A1 N4
[4 marks]
correct AP or GP (A1)
eg finding common difference is \(3\), common ratio is \(2\)
valid approach using arithmetic and geometric formulas (M1)
eg \(1 + 3(n - 1)\) and \({r^{n - 1}}k\)
\({u_n} = 3n - 2 + {2^{n - 1}}k\) A1A1 N4
Note: Award A1 for \(3n - 2\), A1 for \({2^{n - 1}}k\).
[4 marks]
