This week in Precalc 11 we learned about Geometric Sequences (patterns that multiply by the same number to get the next number), Finite Geometric Series (patterns that don’t have numbers that eventually start to look the same), and Infinite Geometric Sequences (patterns that never have an ending, but still possible to find the sum because eventually the numbers in the sequence become very close together). The one thing that stood out to me is finding the finite geometric series.

When given a geometric sequence, just like an arithmetic sequence, it’s possible to find the sum of it. Finding it for an arithmetic sequence, though, is different than finding it for geometric sequence. For example, if you need to find S_{12} of a geometric series you don’t need to find t_{12} first like for an arithmetic series. Instead, you can just plug in what you know into the equation given.

Ex.

Explanation:

Step 1: Find the common ratio

Common ratio is different than the common difference that we were introduced to in the arithmetic unit. Instead of finding the number that the numbers go up by each time, we find the number that is used to multiply the last number to get the next number.

Step 2: Find S_7

Once we know what the common ratio is, then we have everything we need to fill in the equation to get the answer we are looking for.