C1 January 2005 Q5
5. The \(r\)th term of an arithmetic series is \((2r - 5)\).
(a) Write down the first three terms of this series. (2)
(b) State the value of the common difference. (1)
(c) Show that \(\displaystyle\sum_{r=1}^{n}(2r - 5) = n(n - 4)\). (3)
| Scheme | Marks |
|---|---|
| \(-3,\ -1,\ 1\) B1: One correct | B1 B1 |
| (2) |
| Scheme | Marks |
|---|---|
| 2 (ft only if terms in (a) are in arithmetic progression) | B1ft |
| (1) |
| Scheme | Marks |
|---|---|
| \(\text{Sum} = \dfrac{1}{2}n\{2(-3) + (n - 1)(2)\}\) or \(\dfrac{1}{2}n\{(-3) + (2n - 5)\}\) | M1 A1ft |
| \(= \dfrac{1}{2}n\{2n - 8\} = n(n - 4)\) (*) | A1 |
| (3) | |
| (6 marks) |