Higher June 2024 Paper 3 Q20
20 \(x - 4\), \(x + 2\) and \(3x + 1\) are three consecutive terms of an arithmetic sequence.
(a) Find the value of \(x\). (2)
\(y - 4\), \(y + 2\) and \(3y + 1\) are three consecutive terms of a geometric sequence.
(b) Find the possible values of \(y\). (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 3.5 | P1 | for process to find the common difference between the first and second and the common difference between the third and second term eg \((3x + 1) - (x + 2)\ (= 2x - 1)\) and \((x + 2) - (x - 4)\ (= 6)\) or for process to write a correct equation in \(x\), eg \((3x + 1) - (x + 2) = (x + 2) - (x - 4)\) or \(2x - 1 = 6\) oe |
| A1 | for 3.5 oe eg \(\dfrac{7}{2}\) |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(-0.5\), 8 | P1 | for process to write a correct equation in terms of the common ratio and \(y\) eg \(r(y - 4) = y + 2\) or \(r(y + 2) = 3y + 1\) |
| P1 | for process to write a correct equation in \(y\) eg \(\dfrac{3y + 1}{y + 2} = \dfrac{y + 2}{y - 4}\) oe | |
| P1 | for process to write a correct equation without fractions eg \((3y + 1)(y - 4) = (y + 2)(y + 2)\) oe | |
| P1 | for process of writing a correct simplified equation eg \(2y^2 - 15y - 8\ (= 0)\) | |
| A1 | cao |
Additional guidance
\(r\) can be any letter apart from \(y\)
The quadratic does not have to equal 0, ie accept \(2y^2 - 15y = 8\)