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?

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Uniteasy Admin · Accepted 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

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