3.1 Sequences and Summation Notation
One of the most famous sequences in the world is the Fibonacci sequence. The sequence is an infinite sequence that begins as follows:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...
Every term after the first two terms are the sum of the two proceeding terms. But the more interesting thing about the Fibonacci sequence is how often the numbers appear in nature.
When we write the terms of a a sequence, all we do is plug in "n" where appropriate.
Recursion formulas are one of the easier sequences, because each term uses the term prior in order to calculate it.
We have used factorial notation before while computing permutations and combinations. All we do is multiply from the number down to 1. For example:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Probably the most confusing part of sequences is the introduction of summation notation. Summation notation uses the Greek letter Sigma. It is an abbreviated way to write out finding the sum of a finite sequence. You will see sigma notation on college placement tests and in college classes.
If you need additional help on any of these topics, here is an additional video that covers the entire section.