Summation chart

A chart used to determine the number of ranks required to attain a bonus, based on an incremental additive scale. It is used particularly for Lore bonuses in certain spells. To use the chart all you need to know is the amount of training first needed to see a bonus, also known as the Seed.

Another way to calculate any value on the chart:

X	Bonus
Y	Seed
Z	Ranks Needed

 Z = (X^2 - X) / 2 + XY

 Y = -(X^2 - X - 2Z) / 2X

 X = (sqrt(4Y^2 - 4Y + 8Z + 1) - 2Y + 1) / 2

Resources

http://www.play.net/gs4/info/spells/lores.asp#Summation - The summation chart