Posted by **Marcel** on Thursday, February 11, 2010 at 12:53am.

You have 798 cans in 19 rows. If the cans are placed so that each row as 3 fewer cans than the other how many cans are in the bottom row?

- arithmetic -
**Reiny**, Thursday, February 11, 2010 at 8:03am
This is an arithmetic series

You know S_{19}, n=19, d=-3

You don't know "a".

S_{19}= (n/2)[2a + (n-1)d]

798 = 19/2(2a + 18(-3)]

1596 = 38a - 1026

2633 = 38a

a = 69

So depending on whether your bottom row is the

first or the 69th, it would be either 69 or

69 + 18(-3) = 15

check:

69 + 66 + 63 + ... + 15 for 19 terms

= 19(first+last)/2 = (19)(69+15)/2 = 798

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