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How much money would you have if the amount of money you started with was 5 and it increased by 5 a day for 365 days. So January 1st you receive 5, Jan 2nd you receive 10, the third 15.. etc. I'm wondering what the formula is

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    Try [this](http://math.stackexchange.com/q/59443/6179).2012-01-21

2 Answers 2

5

Hint: On the 365th day, you will receive $365*5=1825$ dollars. Then the total amount of money is

$5+10+15+\cdots+1820+1825.$ Consider double this amount. That is consider $\begin{array}{ccccccc} 5 & +10 & +15 & +\cdots & +1815 & +1820 & +1825\\ 1825 & +1820 & +1815 & +\cdots & +15 & +10 & +5\end{array}$

Adding up the rows we get $1830+1830+1830+\cdots+1830+1830+1830$

$=365*1830.$ Now take this and divide it by 2. Then we have the original sum.

See also: Arithmetic Progression.

Hope that helps,

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$5 + 2\times 5 + 3\times 5 + \cdots + 365\times 5 = 5\times\Bigl( 1+2+\cdots + 365\Bigr)$ at which point it comes down to figuring out how much is the sum of $n$ consecutive integers, starting with $1$.