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
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•
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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.)