Higher November 2024 Paper 2 Q15
15 Here are the first five terms of a quadratic sequence.
3 20 47 84 131
(a) Find an expression, in terms of \(n\), for the \(n\)th term of this sequence. (3)
The terms of a different sequence are given by the rule \(u_{n+1} = ku_n + k\) where \(k\) is a constant.
Given that \(u_1 = 9\) and \(u_2 = 4\)
(b) find the value of \(u_4\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(5n^2 + 2n - 4\) | M1 | for a correct start to a method to find the \(n\)th term, eg constant 2nd differences and \(n^2\) OR states \(2a = 10\) or \(3a + b = 17\) |
| M1 | for working with \(5n^2\), eg \(5n^2\), and sequence \(-2, 0, 2, \ldots\) OR states \(2a = 10\) and \(3a + b = 17\) | |
| A1 | for \(5n^2 + 2n - 4\) oe |
Additional guidance
Need to see constant 2nd difference found and \(n^2\)
Condone use of a different variable throughout
\(a = 5\) or \(b = 2\) implies M1
\(5n^2 + 2n\) implies M2
\(5n^2\) is implied by \(5, 20, 45, \ldots\)
\(a = 5\) and \(b = 2\) implies M2
Condone \(+\,-4\)
| Answer | Mark | Mark scheme |
|---|---|---|
| 1.2 | M1 | for substituting values, eg \(4 = k \times 9 + k\) or \(4 = k(9 + 1)\) or \((k = 0.4)\) |
| M1 | for \((u_3 =)\ \text{``}0.4\text{''} \times 4 + \text{``}0.4\text{''}\ (= 2)\) | |
| A1 | for 1.2 oe |