Special Patterns

You now have examined both sequences without patterns and sequences with predictable patterns. In the remainder of this module, you will work with sequences that have one of two identifiable special patterns: (1) each term has the same number added to it to find the next term; and (2) each term is multiplied by the same number to find the next term.

Consider this sequence: 6,3,0,-3,-6,-9,... Can you describe the pattern as you move from one term to the next? A careful analysis shows that, in each instance, you are adding -3 to each term to determine the next term.

Now analyze this sequence: 6,12,24,48,96, ... What is happening here? As you move from one term to the next, you are multiplying the preceding term by 2.

Look for these special patterns in the next topics in this module.