Final Fantasy XIII: Capped Weapon experience equation
This is an equation to understand how much experience you will need to spend to get any weapon capped at its current level:
n = Increase your weapon will grow after every level obtain. For example, at level 1 to 2 you need 1,000 experience. From level 2 to 3 you need 1,125 exp. n = 1125 minus 1000, which in this case is 125. So n for this weapon would equal 125.
x = The total number of levels you will need to cap (Star) your weapon. For example, from 1 to 21 (Star) for Tier 1 weapons requires 20 levels (21-1=20).
b = The base experience that your weapon has. For example, Axis Blade at level one needs 1,000 experience to reach level 2. 1,000 is the base experience.
The equation is as follows to determine how much experience it will cost to cap your weapon.
(xn-n)(x/2)+bx = Total experience to cap a weapon.
An easier way to consider this is x times n minus n. Then multiply that value by x divided by 2. Then, add b times x.