How do you calculate the number of cans in this arithmetic progression?

Cans are arranged in a pile such that each row has one less can than the row below. There is a total of 3240 cans in the pile. How many cans are there in the bottom row?

1 Answer
Jan 5, 2018

8080

Explanation:

If there is one can in the top row and there are nn rows, then there are nn cans in the bottom row and the total number of cans would be:

1/2 n (n+1)12n(n+1)

So let's try to solve:

3240 = 1/2 n(n+1)3240=12n(n+1)

Multiply both sides by 22 to get:

6480 = n(n+1)6480=n(n+1)

Note that 6480 = 6400+80 = 80^2+80 = 80(80+1)6480=6400+80=802+80=80(80+1)

So there are 8080 rows of cans with 8080 in the bottom row.