2. A supermarket display consists of boxes of cereal. The bottom row has 23 boxes. Each row has three fewer boxes than the row below it. The display has six rows.

Question

1.    A supermarket display consists of boxes of cereal. The bottom row has 23 boxes. Each row has three fewer boxes than the row below it. The display has six rows.

(A)Write and use a function to determine how many boxes are in the top row. Show your work.

(B)Use the appropriate formula to determine the number of boxes in the entire display. Show your work.

Answer 1

A)

This is a function of the number of rows r

The first row has a fixed number and diminishes by 3 for each row, thus the first row has to be counted out, then multiplied by the diminishing factor and subtracted from the base row.

t(r) = 23 - (r-1) * 3

t(6) = 23 - 5 * 3 = 23 - 15 = 8 on the top row

B)

This is a summation series from the number in the base row b and the number in the top row t

This is the average of the first and last elements times the number of elements, in this case rows r

r * (b + t) / 2

We know that b = 23 and the function for t is the answer to the previous part. The total number n isthe composition of these functions.

n(r) = r * (23 + (23 - (r - 1) * 3)) / 2

n(6) = 6 * (23 + (23 - (5) * 3)) / 2

= 6 * (23 + 8) / 2

= 6 * 15.5

= 93