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thody · Nov 15, 2009, 10:04 AM

Hey... mathematically challenged here. I'm trying to figure out the following. Let's say I want to increase something by 4 each week but also keep the increases from the previous weeks and then get a grand total at the end. Let me show you below using 52 periods.

4 + (4x2) + (4x3) + (4x4) + (4x5)... + (4x52) =??

Right now I know I can just do 52 calculations and add them all together to get my answer but I'm wondering if there is a quicker/easier way. Thanks in advance for any help!

galactus · Nov 15, 2009, 11:38 AM

You want the sum of the first 52 integers multiplied by 4. Yes, there is an easier way.

The sum of the first n integers can be found from the formula $\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$

Your n is 52.

So, we have $4\cdot\frac{n(n+1)}{2}$

$\frac{4\cdot 52\cdot 53}{2}=2\cdot 52\cdot 53=5512$

thody · Nov 15, 2009, 11:44 AM

Originally Posted by galactus

You want the sum of the first 52 integers multiplied by 4. Yes, there is an easier way.

The sum of the first n integers can be found from the formula $\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$

Your n is 52.

So, we have $4\cdot\frac{n(n+1)}{2}$

$\frac{4\cdot 52\cdot 53}{2}=2\cdot 52\cdot 53=5512$

Thanks so much!