An office building has 5 floors. It accommodates 143 employees on the first floor, 118 employees onthe second floor and 93 employees on the third floor. If the number of employees on each floor followsan arithmetic sequence, find the number of employees that can be accommodated on the 4th and 5thfloor of the building
Question
An office building has 5 floors. It accommodates 143 employees on the first floor, 118 employees onthe second floor and 93 employees on the third floor. If the number of employees on each floor followsan arithmetic sequence, find the number of employees that can be accommodated on the 4th and 5thfloor of the building
Solution
In an arithmetic sequence, the difference between any two successive terms is constant. This difference is also known as the common difference.
From the problem, we know that the number of employees on the first floor is 143, on the second floor is 118, and on the third floor is 93.
To find the common difference, we subtract the number of employees on the second floor from the number of employees on the first floor:
143 - 118 = 25
To confirm that this is an arithmetic sequence, we also subtract the number of employees on the third floor from the number of employees on the second floor:
118 - 93 = 25
Since the differences are the same, we can confirm that this is indeed an arithmetic sequence with a common difference of -25.
To find the number of employees on the 4th floor, we subtract the common difference from the number of employees on the 3rd floor:
93 - 25 = 68
Similarly, to find the number of employees on the 5th floor, we subtract the common difference from the number of employees on the 4th floor:
68 - 25 = 43
So, the office building can accommodate 68 employees on the 4th floor and 43 employees on the 5th floor.
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