Module 1: Basic Set Theory
Set Operations
4 Topics
Module 2: Modular Arithmetic, Divisibility, and the Fundamental Theorem of Arithmetic
Module 3: Functions and Relations
Functions Basics
4 Topics
Module 4: Truth Tables and Symbolic Logic
Truth Tables
2 Topics
Conditional Statements
2 Topics
Module 5: Basic Direct Proofs
Basic Direct Proofs
3 Topics
Module 6: Proof Techniques Part 1: Contrapositive and Contradiction
Module 7: Sequences, Sums, and Products
Module 8: Proof Techniques Part 2: (Weak) Induction
Module 9: Recurrence Relations and Recursion
Module 10: Counting Systems (Binary, Hex, Octal, etc.)
Arithmetic in Binary
4 Topics
Module 11: Combinatorics
Module 12: Graph Theory
Paths and Circuits
2 Topics
Module 13: Review
Arithmetic and Geometric Sequences and Sums
In the following sequences, see if you can determine a pattern than would allow you to find the next three entries of the sequence (assuming of course that the sequence continues according to that rule).
$$A=\{1,4,7,10,13, 16,19,…\}$$
$$B=\{1,3,9,27,81,…\}$$
You may notice that, in \(A\), every pair of consecutive entries in the sequence differ by \(3\). So, to go from one entry to the next, one simply adds \(3\) repeatedly. This sort of sequence is called an arithmetic sequence.
In \(B\), it appears that in order to go from \(1\) to \(3\) or from \(3\) to \(9\), and so on, one must repeatedly multiply by the same number, in this case \(3\). Sequences that work like this are called geometric sequences.