Question: An iterative formula is shown below. $x_{n+1} = 2x_n$ Starting with $x_1 = 4$, calculate the values of $x_2$, $x_3$ and $x_4$. A taxi journey has an initial charge of 2 plus 0.40 for every mile travelled. Work out the distance travelled for a journey that costs 6.40.

1. **Problem 1: Iterative formula calculation** Given the iterative formula: $$x_{n+1} = 2x_n$$ and the starting value: $$x_1 = 4$$ Calculate $x_2$, $x_3$, and $x_4$. 2. **Formula and rules:** The formula means each next term is twice the previous term. 3. **Calculate $x_2$:** $$x_2 = 2x_1 = 2 \times 4 = 8$$ 4. **Calculate $x_3$:** $$x_3 = 2x_2 = 2 \times 8 = 16$$ 5. **Calculate $x_4$:** $$x_4 = 2x_3 = 2 \times 16 = 32$$ --- 6. **Problem 2: Taxi journey distance calculation** The cost formula is: $$\text{Cost} = 2 + 0.40 \times \text{miles}$$ Given the total cost is 6.40, find the distance travelled. 7. **Set up the equation:** $$6.40 = 2 + 0.40 \times \text{miles}$$ 8. **Isolate miles:** $$6.40 - 2 = 0.40 \times \text{miles}$$ $$4.40 = 0.40 \times \text{miles}$$ 9. **Divide both sides by 0.40:** $$\frac{4.40}{\cancel{0.40}} = \frac{0.40 \times \text{miles}}{\cancel{0.40}}$$ $$11 = \text{miles}$$ **Final answers:** - $x_2 = 8$ - $x_3 = 16$ - $x_4 = 32$ - Distance travelled = 11 miles