Sequences

What is a sequence? What is a term? 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 +4 +4 +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 2nd term minus the 1st term.

Arithmetic Sequence the same number each time 2, 4, 6, 8, … 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,… 27, 24, 21, 18,… 5, 20, 35, 50,… Common difference: + 3 27, 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 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 x3 x3 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 2nd term divided by the 1st term.

Geometric Sequence by the same number each time 1, 4, 16, 64, … Multiply by the same number each time This is called the common ratio examples 1, 4, 16, 64, … common ratio is x 4 400, 200, 100, 50, … common ratio is x 𝟏 𝟐 or x o.5

Geometric Sequence 4, 8, 16, 32, 64, 128,… Common ratio: x 2 2000, 1000, 500, 250, 125, 62.5,… Common ratio: x ½ or x 0.5 6, 24, 96, 384, 1536, 6144,… Common ratio: x 4

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

Arithmetic Geometric Make your own patterns 1st term: 1, n + 2

terms that are next to each other 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… 2n 16, 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

What is the next term in this sequence? 5, -1, -7 -13 , _____ -6 -6 -6 -6 -19

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

What is the next term in this sequence? -400,-380,-360,-340 , ____ +20 +20 +20 +20 -320

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

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