| Date | November 2008 | Marks available | 3 | Reference code | 08N.1.sl.TZ0.8 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 8 | Adapted from | N/A |
Question
Given the arithmetic sequence: \({u_1} = 124{\text{, }}{u_2} = 117{\text{, }}{u_3} = 110{\text{, }}{u_4} = 103, \ldots \)
Write down the common difference of the sequence.
Calculate the sum of the first \(50\) terms of the sequence.
\({u_k}\) is the first term in the sequence which is negative.
Find the value of \(k\).
Markscheme
\(d = - 7\) (A1) (C1)
[1 mark]
\({S_{50}} = \frac{{50}}{2}(2(124) + 49( - 7))\) (M1)
Note: (M1) for correct substitution.
\( = - 2375\) (A1)(ft) (C2)
[2 marks]
\(124 - 7(k - 1) < 0\) (M1)
\(k > 18.7\) or \(18.7\) seen (A1)(ft)
\(k = 19\) (A1)(ft) (C3)
Note: (M1) for correct inequality or equation seen or for list of values seen or for use of trial and error.
[3 marks]
Examiners report
(a) Again, the omission of the negative sign was a too common fault.
This was generally well attempted.
The common misconception was confusion between \(k\) and the value of the \(k\)th term. Close reading of this part was required from the candidates.
