Higher June 2018 Paper 1 Q20
20 A linear sequence starts
\[a + 2b \qquad a + 6b \qquad a + 10b \qquad \ldots\ldots \qquad \ldots\ldots\]The 2nd term has value 8
The 5th term has value 44
Work out the values of \(a\) and \(b\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| (5th term \(=\)) \(a + 10b + 4b + 4b\) or (5th term \(=\)) \(a + 18b\) | M1 | oe |
| \(a + 6b = 8\) and \(a + 18b = 44\) | M1dep | oe correct simultaneous equations eg \(3a + 18b = 24\) and \(a + 18b = 44\) implied by \(12b = 36\) or \(2a = -20\) |
| \(b = 3\) or \(a = -10\) | A1 | |
| \(a = -10\) and \(b = 3\) | A1 | |
| Alternative method 2 | ||
| (\(d =\)) \(\dfrac{44 - 8}{3}\) or (\(d =\)) \(\dfrac{36}{3}\) or (\(d =\)) 12 | M1 | any letter |
| \(4b = 12\) | M1dep | oe |
| \(b = 3\) | A1 | |
| \(a = -10\) and \(b = 3\) | A1 | |
Additional guidance
| Correct substitution without writing simultaneous equations scores the first two marks on alt 1 eg (\(a = 8 - 6b\) and) \(8 - 6b + 18b = 44\) | M1M1 |