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!

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

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!