Higher November 2017 Paper 2 Q23
23 S is a geometric sequence.
(a) Given that \((\sqrt{x} - 1)\), 1 and \((\sqrt{x} + 1)\) are the first three terms of S, find the value of \(x\).
You must show all your working. (3)
You must show all your working. (3)
(b) Show that the 5th term of S is \(7 + 5\sqrt{2}\) (2)
| Answer | Mark | Notes |
|---|---|---|
| 2 | M1 | for start to express the common ratio algebraically, eg \(1/(\sqrt{x} - 1)\) or \((\sqrt{x} + 1)/1\) or \(\sqrt{x} + 1 = k \times 1\) or \(1 = k \times (\sqrt{x} - 1)\) |
| M1 | for setting up an appropriate equation in \(x\), eg \(1/(\sqrt{x} - 1) = (\sqrt{x} + 1)/1\) | |
| C1 | for convincing argument to show \(x = 2\) |
| Answer | Mark | Notes |
|---|---|---|
| Shown | M1 | for expressing the relationship between the common ratio, one of the first three terms of the sequence and the fifth term, eg 5th term = 3rd term × (common ratio)² |
| C1 | for a complete explanation to include eg, \((\sqrt{2} + 1)(\sqrt{2} + 1)^2 = 7 + 5\sqrt{2}\) |