This was week 1 of Pre-Calc 11 and so far, I am enjoying it! We’ve started off with arithmetic sequences and arithmetic series. The difference between the two is that in an arithmetic sequence, you are either adding or subtracting the same difference to your starting number. In a series, you are adding all the numbers in the sequence together to get a total.
One thing that really stuck out to me over the week was learning about Arithmetic series and how arithmetic progression works. I know that’s a lot of “arithmetic” but bear with me, please. There was a little boy named Johann Carl Friedrich Gauss (Pretty awesome name, right?) In the late 1700s, Johann was at school and pestering his teacher endlessly to give him more difficult math work. Back then, a school a little one-room building with a myriad of grades inside, so that teacher must have been stressed enough as it is. Hoping to get Johann to leave him alone for a while, he told him to add all the numbers together from 1-100. This means that a kid is going to have to add every number together (1+2+3+4+5…97+98+99+100). Under normal circumstances, this should have taken a long time, but Johann was actually a bit of a genius. He came back a couple minutes later with it all added up. The teacher didn’t believe him because there was no way a child could figure it out that quickly, right? Well, wrong as it turns out.
This is generally how Johann solved it so quickly.
First of all, BEDMAS states that addition and subtraction have equal “value” in an equation. Because there is only addition used in an arithmetic series, you can add any of the numbers to each other in whatever order you want. What Johann figured out is instead of doing it the messy way of starting at one and adding everything together:
He could add each number on the end to each other, and come up with the same number!!
Since you are adding two numbers together each time, (
I found this a really cool use of math and even surprised myself when I tried it and found out it was indeed right! I am looking forward to the weeks to come and what other cool topics we’ll cover.