Higher June 2018 Paper 2 Q23
23 The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series.
Find the sum of the first 30 terms of this series.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{48}{2}(2a + (48 - 1)d)\) or \(\dfrac{36}{2}(2a + (36 - 1)d)\) oe | M1 |
| \(\dfrac{48}{2}(2a + (48 - 1)d) = 4 \times \dfrac{36}{2}(2a + (36 - 1)d)\) oe | M1 |
| \(96a + 1392d = 0\) oe eg \(4a + 58d = 0\), \(2a + 29d = 0\) or \(a = -14.5d\) etc | M1 |
| \(\dfrac{30}{2}(2a + (30 - 1)d)\) | M1 |
| 0 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: For a correct expression for the first 48 terms or the first 36 terms
M1: For a correct equation.
M1: Indep Allow substitution of any ‘found’ values of \(a\) and \(d\)