There are eight shelves. How many soup cans a grocery clerk stack if the bottom shelf has 21 cans and each additional shelf has 2 fewer soup cans than the previous shelf?
21 + 19 + 17 ...
a (a+d) (a + 2d) ..... a+7d eight terms
where
a = 21
and
d = -2
arithmetic series
sum of first 8 = (8/2) (42 + 7(-2) )
= 4 (42 - 14)
= 4 (28)
= 112
To find the number of soup cans stacked on each shelf, we'll start with the bottom shelf and subtract 2 cans for each additional shelf.
The number of soup cans on each shelf can be represented as a sequence or list. Let's write down the number of cans on each shelf:
Bottom shelf: 21 cans
Second shelf: 21 - 2 = 19 cans
Third shelf: 19 - 2 = 17 cans
Fourth shelf: 17 - 2 = 15 cans
Fifth shelf: 15 - 2 = 13 cans
Sixth shelf: 13 - 2 = 11 cans
Seventh shelf: 11 - 2 = 9 cans
Eighth shelf: 9 - 2 = 7 cans
So, the list of the number of soup cans stacked on each shelf is 21, 19, 17, 15, 13, 11, 9, 7.
To find the total number of soup cans stacked by the grocery clerk, we sum up all the cans on each shelf:
21 + 19 + 17 + 15 + 13 + 11 + 9 + 7 = 112.
Therefore, the grocery clerk will stack a total of 112 soup cans.