This video is all about two very special Recursive Sequences: Arithmetic and Geometric Sequences.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
A Recursive equation is a formula that enables us to use known terms in the sequence to determine other terms.
An Arithmetic Sequence is such that each term is obtained by adding a constant to the preceding term. This constant is called the Common Difference.
Whereas, in a Geometric Sequence each term is obtained by multiply a constant to the preceding term. This constant is called the Common Ratio.
In the beginning we will learn how to write terms for an Arithmetic or Geometric Sequence when we are given either the common difference or the common ratio.
Next we will utilize the General Formulas for both the Arithmetic and Geometric Sequences and use them to find any term in the sequence, as well as the nth term.
Comparing Arithmetic and Geometric Sequences
It’s going to be very important for us to be able to find the Common Difference and/or the Common Ratio. So how do we go about doing this?
Well, all we have to do is look at two adjacent terms. And adjacent terms, or successive terms, are just two terms in the sequence that come one right after the other.
Then, we either subtract or divide these two adjacent terms and viola we have our common difference or common ratio.
And it’s this very process that gives us the names “difference” and “ratio”.
I like how Purple Math so eloquently puts it: if you subtract (i.e., find the difference) of two successive terms, you’ll always get a common value, and if you divide (i.e., take the ratio) of two successive terms, you’ll always get a common value.
Then we will investigate different sequences and figure out if they are Arithmetic or Geometric, by either subtracting or dividing adjacent terms, and also learn how to write each of these sequences as a Recursive Formula.
And lastly, we will look at the famous Fibonacci Sequence, as it is one of the most classic examples of a Recursive Formula.
Geometric Sequences – Video
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