If I saved a dollar on the first day of the year and saved two dollars on the second, and continued this pattern,how many dollars would I have on the 268th day.

Question

I need to know how much I should have saved by now.

Answer 1

If you were to saved 1 dollar on the first day of the year then 2 dollar on the second day, etc

 

1,2,3,4,.....268

This is called an "Arithmetic series"

 

S=1+2+3+.......+268

The sum S, is called the partial sum and is given by:

 

S_n=(n/2)(a₁+a_n)

 

So here

n=Total number of day = 268

a₁ = first term = 1

a_{n= last term= 268}

 

S_n=(268/2)(1+268)

 

   =( 134)(269)

   =36,046

So you must save $36,046