Week 2 – Precalc 11

This week in math we learned about geometric sequences. For the sequence to be geometric, each term must be multiplied by a constant, known as the common ratio, or ‘r’. You can use the equation r=$\frac{t_n}{t_{n-1}}$ to find r, the common ratio in order to tell if it’s a geometric sequence. You can insert any two consecutive terms into $t_n$ and $t_{n-1}$. If all the terms in the sequence you are give have the same common ratio, then it is a geometric sequence.

Here is an example: 8, 24, 72, 216, …

r=$\frac{t_n}{t_{n-1}}$

r=$\frac{24}{8}$

r=3

Now, check to see if the other terms have the same common ratio: $\frac{72}{24}$=3, $\frac{216}{72}$=3. Yes, it is a geometric sequence because each term has the same common ratio.

We know how to tell if a sequence is geometric and we know how to find the common ratio, r. So, below is an example of how you can use this information to find a certain term number in a geometric sequence. We’ll be using the equation $t_n$=a·$r^{n-1}$. Something important to note is that a=the first term in the sequence.