Understanding what a Sequence is and how it is generated is an extremely important topic not only in mathematics but also in every day life.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
A Sequence is nothing more than a listing of numbers that follow a specified pattern.
We are going to learn how to generate the Explicit Formula or Equation for a sequence that identifies how each term in the sequence is generated, and see how we can then use these terms to produce a graph.
Some textbooks will refer to the Explicit Formula as the General Term or Rule, as Math is Fun accurately states.
All this means is that we are trying to figure out the pattern of the numbers in the sequence.
We will look at some tricks that will helps us in creating our Rule, and we will continue to add to our skill set with each subsequent lesson.
Definition of a Finite Sequence
Next, we will look at the two major types of sequences: Finite and Infinite.
A Finite Sequence is one that is bounded or stops.
And an Infinite Sequence is one that is unbounded or goes on forever.
For example, the days in a week {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} is an example of a Finite Sequence because there are only seven possible days.
Whereas, all the odd numbers {1, 3, 5, 7, 9, … } is an example of an Infinite Sequence because it goes on forever.
This will lead us to a discussion of important terms like:
- Convergence
- Divergence
- Alternating
- Recursive
- Monotonic
While we will not use a formal proof for determining Convergence or Divergence for a Sequence as it needs calculus and the Nth-term Test for Sequences, we will still be able to see if a Sequence will converge or diverge and whether it is alternating, increasing or decreasing just by looking at a list of Partial Terms.
We will also learn how to determine if a Sequence is Monotonic by comparing two adjacent terms.
Additionally, we will also learn how to use Factorials and apply them to expressions as well as Sequences.
Introduction to Sequences – Video
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