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
calculating money after 365 days if payment increased $5 per day
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algebra-precalculus
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0Try [this](http://math.stackexchange.com/q/59443/6179). – 2012-01-21
2 Answers
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,
3
$5 + 2\times 5 + 3\times 5 + \cdots + 365\times 5 = 5\times\Bigl( 1+2+\cdots + 365\Bigr)$ at which point it comes down to figuring out how much is the sum of $n$ consecutive integers, starting with $1$.