| Date | May 2014 | Marks available | 6 | Reference code | 14M.2.hl.TZ2.1 |
| Level | HL only | Paper | 2 | Time zone | TZ2 |
| Command term | Express and Find | Question number | 1 | Adapted from | N/A |
Question
(a) (i) Find the sum of all integers, between 10 and 200, which are divisible by 7.
(ii) Express the above sum using sigma notation.
An arithmetic sequence has first term 1000 and common difference of −6 . The sum of the first n terms of this sequence is negative.
(b) Find the least value of n.
Markscheme
(a) (i) \(n = 27\) (A1)
METHOD 1
\({S_{27}} = \frac{{14 + 196}}{2} \times 27\) (M1)
\( = 2835\) A1
METHOD 2
\({S_{27}} = \frac{{27}}{2}(2 \times 14 + 26 \times 7)\) (M1)
\( = 2835\) A1
METHOD 3
\({S_{27}}\sum\limits_{n = 1}^{27} {7 + 7n} \) (M1)
\( = 2835\) A1
(ii) \(\sum\limits_{n = 1}^{27} {(7 + 7n)} \) or equivalent A1
Note: Accept \(\sum\limits_{n = 2}^{28} {7n} \)
[4 marks]
(b) \(\frac{n}{2}\left( {2000 - 6(n - 1)} \right) < 0\) (M1)
\(n > 334.333\)
\(n = 335\) A1
Note: Accept working with equalities.
[2 marks]
Total [6 marks]
