Suppose that you play black jack at Harrah's on June 1 and lose $1,000. Tomorrow you bet and lose $15 less. Each day you lose $15 less that your previous loss. What will your total losses be for the 30 days of June?

#### Question

#### Answer

As each day you lose $15 less that your previous loss, this is an arithmetic sequence and the difference between any two successive terms is -15. So,

a_1=1000

and

d=-15

The formula for general terms is

a_n=a_1+(n-1)d = 1000+(n-1)(-15) = -15n+1015

a_{30} = -15(30)+1015=565

Calculate the 30th partial sum as follows:

S_{30} = \dfrac{30(a_1+a_{30})}{2}=\dfrac{30(1000+565)}{2}=23475

So after 30 days you will lose a total of $23,475