Higher January 2021 Paper 1 Q24
24 An arithmetic series has first term \(a\) and common difference \(d\).
The sum of the first \(2n\) terms of the series is four times the sum of the first \(n\) terms of the series.
Find an expression for \(a\) in terms of \(d\).
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{2n}{2}\left[2a + (2n - 1)d\right]\) oe | M1 |
| \(\dfrac{2n}{2}\left[2a + (2n - 1)d\right] = 4 \times \dfrac{n}{2}\left[2a + (n - 1)d\right]\) oe | M1 |
| \(2a - d = 4a - 2d\) oe | M1 |
Working required Answer: \(\dfrac{d}{2}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct expression for \(S_{2n}\)
M1: dep on M1 for setting up a correct equation for \(S_{2n} = 4 \times S_n\)
M1: for a correct linear expression in \(a\) and \(d\)
A1: (dep on M2) for \(\dfrac{d}{2}\) oe