Foundation June 2017 Paper 2 Q20
20.
(a)
The \(n\)th term of a sequence is \(3n - 2\).
Write down the first three terms in the sequence. [2]
(b)
Reza says
‘1000 is in this sequence’
Show that Reza is correct. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 1, 4, 7 ISW | B2 | B1 for 2 correct terms in correct positions. B1 for –2, 1, 4. |
| Scheme | Marks | Comments |
|---|---|---|
| \(3n - 2 = 1000\) | M1 | |
| (\(n =\)) 334 (whole number therefore yes) ‘1000 is the 334th term’ or equivalent | A1 | An answer of 334 implies the M1 mark. |
| (4) |
Alternative
Alternative methods:
Trial and improvement:
B2 for 334. B1 for at least two correctly evaluated trials with \(300 \lt n \lt 400\).
Logic:
| Scheme | Marks |
|---|---|
| e.g. 1002 is a multiple of 3 | B1 |
| so 1002 is in the sequence \(3n\), so 1000 is in the sequence \(3n - 2\). | B1 |