Higher November 2022 Paper 2 Q10
10 The \(n\)th terms of two linear sequences, A and B, are added to give the \(n\)th term of a new sequence.
The new sequence starts
8 13 18 23
The \(n\)th term of sequence A is \(\quad n + 1\)
Work out the \(n\)th term of sequence B. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – Works out \(n\)th term of new sequence | ||
| Common difference of 5 identified | M1 | implied by \(5n \ldots\) |
| \(5n + 3\) | A1 | oe eg \(8 + 5(n - 1)\) |
| their \((5n + 3) - (n + 1)\) | M1 | oe their \((5n + 3)\) must be a linear expression condone missing brackets |
| \(4n + 2\) | A1ft | oe eg \(6 + 4(n - 1)\) ft their \(5n + 3\) which must be a linear expression missing brackets must be recovered |
| Alternative method 2 – Works out terms of sequence A and sequence B | ||
| 2, 3, 4 | M1 | sequence A |
| 6, 10, 14 | A1 | sequence B |
| Common difference of 4 identified | M1 | ft their 6, 10, 14 which must be a linear sequence for B |
| \(4n + 2\) | A1ft | oe eg \(6 + 4(n - 1)\) ft their 6, 10, 14 which must be a linear sequence for B |
Additional guidance
Choose the scheme that favours the student