Let's first find the number of boxes in the top row of the display using the given information.
If the bottom row has 25 boxes, and each row has two fewer boxes than the row below it, then the number of boxes in each row can be represented by a sequence of consecutive even integers. For example, if the bottom row has 25 boxes, then the second-to-bottom row would have 23 boxes (25 - 2), the third-to-bottom row would have 21 boxes (23 - 2), and so on.
We can express the number of boxes in each row using a linear function in the form of y = mx + b, where y is the number of boxes, x is the row number (with x = 1 representing the bottom row), m is the rate of change, and b is the initial value (the number of boxes in the bottom row).
In this case, we know that the bottom row has 25 boxes, and that each subsequent row has two fewer boxes than the row below it. This means that the rate of change is -2 (since the number of boxes decreases by 2 for each row), and the initial value is 25 (since that's the number of boxes in the bottom row). Therefore, we can express the number of boxes in each row using the function:
y = -2x + 25
To find the number of boxes in the top row (which is the seventh row), we can substitute x = 7 into the function:
y = -2(7) + 25
y = -14 + 25
y = 11
Therefore, there are 11 boxes in the top row of the display.
Next, let's use the appropriate formula to determine the total number of boxes in the entire display. Since each row has a decreasing number of boxes, we can use the formula for the sum of an arithmetic sequence to find the total number of boxes:
Sn = (n/2)(a1 + an)
where Sn is the sum of the first n terms of the sequence, a1 is the first term, and an is the nth term.
In this case, we know that there are 7 rows in the display, and that the number of boxes in the bottom row is 25, and the number of boxes in the top row is 11. Therefore, a1 = 25 and an = 11, and n = 7. Substituting these values into the formula, we get:
Sn = (7/2)(25 + 11)
Sn = (7/2)(36)
Sn = 126
Therefore, there are 126 boxes in the entire display.