Higher November 2023 Paper 1 Q25
25 The \(n\)th term of a geometric progression is \(\quad r^n \quad\) where \(\quad r \gt 0\)
The second term is \(\dfrac{8}{9}\)
Work out the third term.
Give your answer in the form \(\quad \dfrac{c\sqrt{2}}{d} \quad\) where \(c\) and \(d\) are integers. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(r^2 = \dfrac{8}{9}\) or \(\sqrt{\dfrac{8}{9}}\) or \(\dfrac{2\sqrt{2}}{\sqrt{9}}\) or \(\dfrac{\sqrt{8}}{3}\) or \(\dfrac{2\sqrt{2}}{3}\) or \(\left(\sqrt{\dfrac{8}{9}}\right)^3\) or \(\dfrac{8\sqrt{8}}{27}\) | M1 | oe eg \(\left(\dfrac{8}{9}\right)^{\frac{1}{2}}\) allow \(\pm\sqrt{\dfrac{8}{9}}\) etc |
| \(\dfrac{16\sqrt{2}}{27}\) | A1 | oe in the form \(\dfrac{c\sqrt{2}}{d}\) where \(c\) and \(d\) are integers |