Higher November 2024 Paper 6 Q9
9 The next term in a Fibonacci sequence is found by adding together the previous two terms.
In a particular Fibonacci sequence:
- the first term is 3
- the second term is \(x\).
(a) Show that the fifth term in the sequence is \(6 + 3x\). [2]
(b) The sixth term in the sequence is 74.
Find the value of \(x\). [4]
Find the value of \(x\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(3 + x\) | 1 | ||
| \(3 + x + 3 + 2x\) [\(= 6 + 3x\)] | 1 | Intent to add correct successive algebraic terms must be clearly conveyed eg  | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 13 nfww | 4 | M2 for \(9 + 5x = 74\) or M1 for \(3 + 2x + 6 + 3x\) or better M1 FT for [\(x =\)] \(\frac{74 - \textit{their } 9}{\textit{their } 5}\) | M2 may be subsequently implied by arithmetic working FT must be from \(ax + b = c\) May be seen in stages as two arithmetic steps or as formal algebra Correct answer from trials scores 4 |