Equation Representing Stock Growth Goal

Nov 2019
1
0
USA
A stock trader starts with a sum of 2500 dollars. His goal is to make 300 the first month, 400 the second month, 500 the third month, and so on. What equation can model this growth to solve for the total amount made after x number of months?
 

romsek

Math Team
Sep 2015
2,679
1,481
USA
I'm using $n$ instead of $x$

$s_n = 2500 + \sum \limits_{k=1}^n 100(k+2)$

$s_n = 2500+100 \left(\dfrac{n(n+1)}{2} + 2n\right) =

2500 + 50n\left(n+5\right)$