Higher June 2017 Paper 3 Q16
16 Using \(x_{n+1} = -2 - \dfrac{4}{x_n^2}\)
with \(x_0 = -2.5\)
(a) find the values of \(x_1\), \(x_2\) and \(x_3\) (3)
(b) Explain the relationship between the values of \(x_1\), \(x_2\) and \(x_3\) and the equation \(x^3 + 2x^2 + 4 = 0\) (2)
| Answer | Mark | Notes |
|---|---|---|
| \(x_1 = -2.64\) \(x_2 = -2.57392\) \(x_3 = -2.603767255\) | M1 | for substitution of \(-2.5\) into the equation (to get \(x_1 = -2.64\)) |
| M1 | for substitution of “\(x_1 = -2.64\)” and “\(x_2 = -2.57392\)” to give \(x_2\) and \(x_3\) | |
| A1 | for \(x_1 = -2.64\) oe, \(x_2 = -2.57(392)\) and \(x_3 = -2.6(03767255)\) Condone \(x_3 = -2.61\) if \(x_2 = -2.57\) is used in the substitution |
| Answer | Mark | Notes |
|---|---|---|
| Statements | C1 | Connection between equation and iterative form in (a) e.g. rearrangement |
| C1 | Statement e.g. iteration is an estimation of a solution |