Section 1.1 Number Patterns Definition: A sequence is an ordered arrangement of numbers, symbols or pictures in which each item or term follows another according to a rule. Examples: (Next term? Rule??) –1,2,3,4, –3,6,9, –1,1,2,3,5, –15,16,18,19,25,26,28,29, Start with 1, add 1 Start with 3, add 3 Fibonacci Sequence: Start with 1 and 1, Add the previous two terms together Start with 15, list numbers with ‘i’ in the word.

A term is a member of a sequence. –t 1 is the first term. –t 2 is the second term. –t n is the n th term. Example: What is t 6 in the sequence 5, 17, 29, 41, ?

An infinite sequence is a sequence that continues on forever. t 1, t 2, t 3, … Note: The three dots indicates the continuation of an infinite sequence. What are the three dots called? Ellipsis Example: –Whole numbers

An finite sequence is a sequence that eventually stops or terminates. t 1, t 2, t 3, …, t n Example: –Digits of number systems Binary Decimal Hexadecimal where t n is the last term of the sequence

Sequence of Differences A sequence that is generated by subtracting each term from the next term. Consider the sequence below: 5, 8, 11, 14, 17, 20,...