June 2023 Paper 2 Q2
2
(a) The first four terms of a linear sequence are\[15 \qquad 18.5 \qquad 22 \qquad 25.5\]
Work out an expression for the \(n\)th term. [2 marks]
(b) A different linear sequence has \(n\)th term \(\quad 318 - 9n\)
Work out the value of the first negative term in the sequence. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(3.5n + 11.5\) | B2 | oe eg \(\dfrac{7n}{2} + \dfrac{23}{2}\) or \(15 + (n - 1) \times 3.5\) B1 linear expression with 3.5 oe as coefficient of \(n\) |
Additional guidance
| For B1 linear expressions may or may not have a constant term eg1 \(3.5n\) eg2 \(15 + 3.5(n + 1)\) (\(3.5n\) implied) | B1 B1 |
| Do not allow the \(n\) term to have the coefficient after \(n\) for B2 eg1 \(n3.5 + 11.5\) eg2 \(n3.5 + 12\) | B1 B1 |
| Allow unambiguous notation eg \(T_n = n \times 3.5 + 11.5\) | B2 |
| Condone \(n =\) or \(= 0\) eg1 \(n = 3.5n + 11.5\) eg2 \(3.5n + 12.5 = 0\) | B2 B1 |
| Condone use of a different variable eg \(N\) or \(x\) | |
| Only identifying common difference of 3.5 | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(-6\) | B2 | B1 \(318 - 9n \lt 0\) oe inequality or \(318 - 9n \leqslant -1\) oe inequality or \(318 \div 9\) oe calculation or \(319 \div 9\) oe calculation or \(35\dfrac{1}{3}\) or 35.3(…) or \(35\dfrac{4}{9}\) or 35.4(…) or 36(th) |
Additional guidance
| B1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Answer \(-6\) | B2 |
| Condone \(n =\) eg1 \(n = -6\) eg2 \(n = 35\dfrac{1}{3}\) | B2 B1 |
| Condone 36(th) and \(-6\) on answer line | B2 |
| \(-6\) in working with 36(th) on answer line | B1 |
| Calculations or values that score B1 may be seen in an equation or an inequality (even if incorrect) eg1 \(n = 106 \div 3\) eg2 \(n \lt 35\dfrac{1}{3}\) | B1 B1 |