Word Problem

[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?

 

[galactus]

\(\displaystyle \L\\\frac{n(n+1)}{2}\)

 

[soroban]

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: $\displaystyle \:100\,+\,200\,+\,300\,+\,400\,+\,\cdots\,+\,10,000$

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


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