1. **Problem Statement:** A computer training course lasts 15 days. Practical training starts at 75 minutes on day 1 and increases by 15 minutes each subsequent day. 2. **Part i) Find the practical training time on the last day:** The time on day $k$ is an arithmetic sequence: $$a_k = a_1 + (k-1)d$$ where $a_1 = 75$ minutes and $d = 15$ minutes. For day 15: $$a_{15} = 75 + (15-1) \times 15 = 75 + 14 \times 15 = 75 + 210 = 285 \text{ minutes}$$ Convert to hours: $$\frac{285}{60} = 4.75 \text{ hours}$$ 3. **Part ii) Show total practical time in $n$ days is $\frac{n}{2}(135 + 15n)$ minutes:** Sum of arithmetic sequence: $$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$ Substitute $a_1=75$, $d=15$: $$S_n = \frac{n}{2}(2 \times 75 + (n-1) \times 15) = \frac{n}{2}(150 + 15n - 15) = \frac{n}{2}(135 + 15n)$$ 4. **Part iii) Find total practical time in hours for 15 days:** Using formula: $$S_{15} = \frac{15}{2}(135 + 15 \times 15) = \frac{15}{2}(135 + 225) = \frac{15}{2} \times 360 = 15 \times 180 = 2700 \text{ minutes}$$ Convert to hours: $$\frac{2700}{60} = 45 \text{ hours}$$ 5. **Part iv) Calculate total amount to pay at 200 per hour:** Total hours = 45 Cost per hour = 200 Total cost: $$45 \times 200 = 9000$$ **Final answers:** - Last day practical time: 4.75 hours - Total practical time in $n$ days: $\frac{n}{2}(135 + 15n)$ minutes - Total practical time for 15 days: 45 hours - Total amount to pay: 9000