Answer:
The difference between the number of rooms on the first and second floor is 18 - 16 = 2.
The difference between the number of rooms on the second and third floor is 16 - 13 = 3.
The difference between the number of rooms on the third and fourth floor is 13 - 9 = 4.
Hence, the pattern is a decreasing arithmetic progression where the difference is increasing by 1 on each consecutive floor.
To find the total number of floors, we need to determine the term where the pattern reaches 0 (since we cannot have negative or zero rooms on a floor). Using the pattern, we can determine that the difference between the fourth and fifth floor would be 9 - 5 = 4. If the difference keeps increasing by 1 after the fourth floor, the fifth floor would have 5 - 4 = 1 room.
Since a floor cannot have 1 room according to the given pattern, we assume that the pattern stops at the fourth floor. Therefore, the building will have a total of 4 floors.
To calculate the total number of rooms, we sum up the number of rooms on each floor:
First floor: 18 rooms
Second floor: 16 rooms
Third floor: 13 rooms
Fourth floor: 9 rooms
Total number of rooms = 18 + 16 + 13 + 9 = 56 rooms
So, the building will have a total of 4 floors and 56 rooms in all.
Explanation: