On a special day at the West Side Market, the grapefruit are arranged in a compact stack of filled-in equilateral triangles with 14 grapefruit on each edge of the bottom triangle, 13 on each edge of the one above, and so on all the way up to the top where there is 1 graperfruit sitting all alone. How many grapefruit are in the entire stack?
Starting at the top, the layers look like this:
,
,
,
,…
The totals of the layers are 1, 1 + 2, 1 + 2 + 3, …, 1 + 2 + … + 14.
You can use the formula 1 + … + n = (n(n + 1))/2 repeatedly to find the total.
You can also use Pascal’s triangle:
1 + 2 + … + 14 = (14 · 15)/2 = 105
The total number of grapefruits is 560.
The total number of grapefruits is 560.