Sequences

What is a sequence? A list of numbers in a certain order. What is a term? One of the numbers in the sequence.

What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. 4, 8, 12, 16, 20………….. +4

What is the common difference? The difference between each number, or what you add each time. 4, 8, 12, 16, 20………….. 4 is the common difference How do you find it? The 2 nd term minus the 1 st term.

Arithmetic Sequence Add the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is 2 50, 40, 30, 20… common difference is -10

Arithmetic Sequences 4, 7, 10, 13,… –Common difference: , 24, 21, 18,… –Common difference: - 3 5, 20, 35, 50,… –Common difference: + 15

Arithmetic Sequences are Linear Patterns When you graph the pattern it makes a line Linear It goes up or down gradually.

What is a geometric sequence? A sequence in which each term can be found by MULTIPLYING the previous term by the same number. 3, 9, 27, 81, 243………….. x3

What is the common ratio? The ratio between each number in the sequence, or what you multiply by each time. 2, 8, 32, 128, 512………….. 4 is the common ratio How do you find it? The 2 nd term divided by the 1 st term.

Geometric Sequence

Geometric Sequences are Exponential Patterns When you graph the pattern it makes a steep curve Exponent ial It goes up or down fast!

Make your own patterns 7.1 st term: 1, 2n 8.1 st term: 1000, 0.5n 9.1 st term: 3, 3n 10.1 st term: 390,625, 0.2n 11.1 st term: 1, 4n 12.1 st term: 100, 1.5n 1.1 st term: 1, n st term: 1000, n + (-50) 3.1 st term: 12, n st term: 81, n + (-9) 5.1 st term: 13, n st term: 20, n + (-4)

Consecutive Terms: terms that are next to each other Variable Expression: can show the rule of a pattern Examples: 2, 4, 6, 8… n+2 8, 6, 4, 2… n + (-2) 2, 4, 8, 16… 2n16, 8, 4, 2… 0.5n

Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference 1

Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio

What is the next term in this sequence? 5, 20, 80, 320, _____ 1,280 x4

What is the next term in this sequence? 5, -1, , _____

What is the next term in this sequence? -3, 6, -12, 24, _____ -48 X-2

What is the next term in this sequence? -400,-380,-360,-340, ____

What is the next term in this sequence? 100, 75, 50, 25____ 0 -25

What is the next term in this sequence? 12, -48, 192, -768____ 3,072 x-4