A store clerk has 99 cans to stack He can fit 24 cans on the

A store clerk has 99 cans to stack. He can fit 24 cans on the bottom row and can stack the cans 6 rows high. Use arithmetic series to determine how he can stack the cans so that each row contains fewer cans than the row beneath it and that the number of cans in each row decreases at a constant rate.

Fill in the blanks:

He can make _____ rows of cans, starting with _____ cans on the bottom. Each row of cans will have _____ fewer cans than the row underneath it.

Solution

solution:

so there are total no. of cans = 99

no. of cans in bottom row = 24

total rows that can be formed= 6

hence it is an arithmetic series

and suppose there is a decrease of \'d\' no. of bottles in each row

hence the series will be

24,(24-d),(24-2d),(24-3d),(24-4d),(24-5d)

now the sum of the series= 99.

now sum of ap is given by

S_n=(n/2)(2a+(n-1)d)

where n are the no. of terms a is initial term and d is common difference

hence in our problem

99=(6/2)(48+5d)

99=3(48+5d)

33=48+5d

5d=-15

d=-3

hence

He can make ___6__ rows of cans, starting with __24___ cans on the bottom. Each row of cans will have ___3__ fewer cans than the row underneath it.