Let's say I want to have saved $200 in one year.
The first week I afford to save $1.
I'm curious to find out how the calculation would look like to understand the following:
By how much would I need to increment the savings each week to reach a total of $200 after 52 weeks?
You could think of it as $\sum\limits_{i=0}^{51}1+ix=200$ or $\sum\limits_{i=1}^{52}1+(i-1)x=200$
Because you're looking to solve $1+(1+x)+(1+2x)+\dots+(1+51x)=200$ for x, right?