A company uses drones to deliver Medical supplies to different locations. On the first day, the drone delivers \(1\) Medical supplies, on the second day it delivers \(2\) Medical supplies, on the third day it delivers \(3\) Medical supplies, and so on. The company delivers a total of \(1275\) Medical supplies over \(n\) days.
Answer the following questions:
1. Determine the number of days \(n\) for which the total number of Medical supplies delivered is \(1275\).
2. Find the number of Medical supplies delivered on the last day.
3. If \(20\%\) of the total Medical supplies records were duplicate entries, find the actual number of distinct grocery orders delivered.
4. Suppose the drone starts recording deliveries from the th day. The numbers of grocery orders delivered from the 15th day. If the total number of grocery orders delivered from the 15th day to the th day is \(1725\), obtain the number of grocery orders delivered on the last day.