Question

The manager of a store is stacking boxes for a display. There are 18 boxes on the bottom row. Each successive row has one less box than the previous row. The expression mc015-1.jpg represents the total number of boxes in the display for the first 15 rows. How many boxes are in the display? 18 22 165 330

Answer 1

(c) 165

Explanation:

You want to know the total number of boxes in 15 rows if the first row has 18 and each succeeding row has 1 less.

Arithmetic sequence

The arithmetic sequence 18, 17, 16, ... has first term a1=18, and common difference d=17-18 = -1. The sum of n terms of it is given by ...

Sn = (2a1 +d(n -1))(n/2)

Application

The first 15 terms of the sequence given here is ...

S15 = (2·18 -1(15 -1))(15/2) = (36-14)(15/2) = 11(15) = 165

There are 165 boxes in the display.