Foundation June 2017 Paper 2 Q11
11
(a) These are the first five terms in a Fibonacci sequence.\[1 \qquad 3 \qquad 4 \qquad 7 \qquad 11\]
Write down the next two terms in the sequence. [1]
(b) In a different Fibonacci sequence the fourth term is 31 and the fifth term is 50.
Work out the first term in this sequence. [2]
(c) The second and third terms in the following Fibonacci sequence are \(x\) and \(y\).
Write down algebraic expressions for the first, fourth and fifth terms.
\[\ldots\ldots\ldots \qquad x \qquad y \qquad \ldots\ldots\ldots \qquad \ldots\ldots\ldots\][3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 18, 29 | 1 | Ignore subsequent terms | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 7 | 2 | M1 for the term before 31 is 19 soi | Condone 7, 12, 19,... for 2 marks. M0 if a 19 is just seen as the difference |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| First term is \(y - x\) | 1 | Condone their correct expressions equated to different variables eg \(2y + x = n\) etc | |
| Fourth term is \(x + y\) | 1 | ||
| Fifth term is \(y + x + y\) or \(2y + x\) oe | 1FT | FT their Fourth term + \(y\) | Their Fourth term an expression in \(x\) and/or \(y\) |