Higher June 2023 Paper 1 Q20
20 The sum of the first 80 terms of an arithmetic series, \(S\), is 470
The 75th term of \(S\) is 14.5
The sum of the first \(X\) terms of \(S\) is 171
Work out the value of \(X\)
Show your working clearly.
(6)
| Scheme | Marks |
|---|---|
| \(\dfrac{80}{2}(2a + 79d) = 470\) oe | M1 |
| \(a + 74d = 14.5\) oe | M1 |
| correct method to find the value of \(a\) or \(d\) eg \(2a + 148d = 29\) – \(2a + 79d = 11.75\) | M1 |
| correct values of \(a = -4\) and \(d = 0.25\) oe | A1 |
| \(\dfrac{X}{2}\left(2 \times \text{``}{-4}\text{''} + (X - 1)\text{``}{0.25}\text{''}\right) = 171\) oe | M1 |
| Working required Answer: 57 | A1 |
| (6) | |
| (6 marks) |
Notes
M1: for substituting into the sum of arithmetic series formula
M1: for substituting into the nth term of arithmetic sequence formula
M1: solve the correct equations simultaneously, eg make the coefficients of \(a\) or \(d\) the same and show the intention to subtract or rearrange one equation to make \(a\) or \(d\) the subject and substitute into the other equation
A1: dep on M2
M1: correctly substituting the found values of \(a\) and \(d\) into a correct equation, can be their values of \(a\) and \(d\) as long as clearly stated
A1: dep on M2