Higher June 2019 Paper 1R Q19
19 The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765
Find the 16th term of the arithmetic series.
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| \(a + 24d = 44.5\) | M1 |
\(\dfrac{30}{2}(2a + (30 - 1)d) = 765\) oe, eg (\(15(2a + 29d) = 765\)), (\(2a + 29d = 51\)), etc | M1 |
| e.g. \(2(44.5 - 24d) + 29d = 51\) oe or \(\begin{aligned} &2a + 48d = 89 \\ -\; &2a + 29d = 51 \end{aligned}\) oe | M1 |
| Working required Answer: 26.5 | A2 |
| (5) | |
| (5 marks) |
Notes
M1: oe
M1: oe (may be simplified)
M1: dep on M2, a complete method to eliminate one variable, allow one arithmetic error
A2: dep on M2, oe
(A1 dep on M2. If not A2, award A1 for \(a = -3.5\) or \(d = 2\))