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,

512

830

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.– t1 is the first term.

– t2 is the second term.

– tn is the nth term.

• Example: What is t6 in the sequence 5, 17, 29, 41, ?

• An infinite sequence is a sequence that continues on forever.t1, t2, t3, …

• 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.t1, t2, t3, … , tn

• Example: – Digits of number systems

• Binary• Decimal• Hexadecimal

where tn 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, . . .