Pre cal application: arithmetic and geometric sequences and series 1. a display of cans on a grocery store consists of 20 cans on the bottom ,18 cans in the next row and so on in an arithmetic sequence, until the top has 4 cans. how many cans in total are in the display

This sequence starts with an initial set; let’s call it s1. This set contains 20 cans, and every set following would have two less cans than the last set. So,

s1=20
s2=s1-2=18
s3=s2-2=16
•
•
•
s9=s8-2=4

How many cans in the display represents the value of each set added together, so we can denote this as

s1+s2+s3+...+s9

and replacing with values:

20+18+16+...+4 = 108

The number of cans in the display equals 108.

(The set notation seems weird, but by practicing this application now, the Calculus version will seem easier.)

The correct answer would be "convenience"