Question

I’m having trouble trying to figure out arithmetic progressions. I’m looking for a formula with an output that increases by 100 more than it’s last increase… like this:

100, 300, 600, 1000, 1500

So the increase pattern looks like this:

(100+)200, (300+)300, (600+)400, (1000+)500, etc

2 hours and 2, front and back, scratch papers have yeilded no such formula. I’m hoping this makes since because my brain is literally fried right now.

This is essentially a level-up formula for an rpg.
When you are level 1 you need 100 exp to level up.
Level 1: 100 (increased by 100)

Level 2: 300 (increased by 200)

Level 3: 600 (increased by 300)

Level 4: 1000 (increased by 400)

and so on…

I don’t feel like hardcoding the levels, so will someone please help me.

Answer 1

write down all your expressions :

level i = leveil i-1 + i*100
level i-1 = level i-2 + i-1 * 100
...
level 1 = level 0 + 100

then summing up these formulas one level k Left hand side eliminate the next one level k right hand side, and you get :

Level i = level 0 + sum(k , k=1 to i)*100

then level i = i*(i+1)/2 *100