| Date | May 2010 | Marks available | 5 | Reference code | 10M.2.hl.TZ1.6 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
Find the sum of all three-digit natural numbers that are not exactly divisible by 3.
Markscheme
\((100 + 101 + 102 + \ldots + 999) - (102 + 105 + \ldots + 999)\) (M1)
\( = \frac{{900}}{2}(100 + 999) - \frac{{300}}{2}(102 + 999)\) M1A1A1
\( = 329\,400\) A1 N5
Note: A variety of other acceptable methods may be seen including for example \(\frac{{300}}{2}(201 + 1995)\) or \(\frac{{600}}{2}(100 + 998)\).
[5 marks]
Examiners report
There were many good solutions seen by a variety of different methods.
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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