Question

if you save one dollar on january 1,two dollars on january 2,three dollars on january 3, and continue this pattern for one year(not a leap year), what will be the value of your entire savings,in dollars, at the end of that one year?

Answer 1

This is an arithmetic progression
\[a_{n}=a_{1}+(n-1)d=1+(364)1=365\]
The sum of a finite arithmetic progression is
\[\S_{n}=\frac{n}{2}(a_{1}+a_{n})=\frac{365}{2}(1+365)=$66,795\]