Answer:
10 boxes in the top row.
192 boxes in entire display.
Step-by-step explanation:
Let n be the number of rows.
Given:
Total number of rows = 8
Boxes in bottom row = 38
And each row has four fewer boxes than the row below it.
Solution:
Part A:
We know that the bottom row has 38 boxes and each row has four fewer boxes than the row below it.
Using below function for determining the number of boxes in each rows.
[tex]f(n)=38-(8-n)4[/tex]
Where:
n = Number of row.
We need to find the boxes in the first row.
So, substitute n = 1 in above function.
[tex]f(1)=38-(8-1)4[/tex]
[tex]f(1)=38-7\times 4[/tex]
[tex]f(1)=38-28[/tex]
[tex]f(1)=10[/tex]
Therefore, 10 boxes in the top row.
Part B:
Total boxes in the entire display.
Using formula as given below to determine the sum of the boxes in entire display.
[tex]S_{n} = \frac{n}{2}(f(1)+f(n))[/tex]
Substitute n = 8, f(1) = 10 and f(8) = 38 in the above equation.
[tex]S_{8} = \frac{8}{2}(10+38)[/tex]
[tex]S_{8} = 4(48)[/tex]
[tex]S_{8} = 4\times 48[/tex]
[tex]S_{8} = 192\ boxes[/tex]
Therefore, 192 boxes in the entire display.
