Week 2 in Pre-Calc has been great! We’ve covered much more in our series and have moved up and on to geometric sequences and series. Those these are fairly basic, I love how they work. Honestly. I find it fascinating that even when you are constantly multiplying, you can have tons of different results.
For instance, let’s say you have a basic sequence of 2, 4, 8, 16…
You know then that the common ratio is 2 because that is what you multiply by each time
However, if you have a sequence of 8, 4, 2, 1, , …
You know* that the common ration is or 0.5
*You can find the common ration by dividing two terms in the sequence. For instance t1 = 8, and t2 = 4. Since the second term is smaller, the common ratio has to be less than 1. You then divide tn by tn-1 (in this case t2/t1) to find your ratio.
Even better is when you have a negative common ratio. Because you are multiplying, a negative times a negative is positive so you may end up with a pattern such as this one:
2, -4, 8, -16, 32, -64…
In this circumstance, the common ratio would be -2.
We also delved into finding fractions from infinite numbers which were very interesting as well.
That’s all for now. Thanks for reading!