Word Problem

lewysangel

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A stockbroker trades stock for 100 days. On day 1 he loses $100. Every day after that, he loses $100 more than on the previous day. What is his average daily loss during the 100 – day period?
 
Hello, lewysangel!

A stockbroker trades stock for 100 days.
On day 1 he loses $100.
Every day after that, he loses $100 more than on the previous day.
What is his average daily loss during the 100–day period?

He loses a total of: 100+200+300+400++10,000\displaystyle \:100\,+\,200\,+\,300\,+\,400\,+\,\cdots\,+\,10,000

. . =  100(1+2+3+4++100)  =  100(1001012)\displaystyle = \;100(1\,+\,2\,+\,3\,+\,4\,+\,\cdots\,+\,100)\;=\;100\left(\frac{100\cdot101}{2}\right)


His average daily loss is: 100(1001012)100  =  1001012  =  $5,050\displaystyle \:\frac{100\left(\frac{100\cdot101}{2}\right)}{100} \;=\;\frac{100\cdot101}{2}\;=\;\$5,050

 
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