Patterns and Sequences sol 6.17 by k woodard and k norman

Arithmetic Sequence the same number each time 2, 4, 6, 8, … Add or Subtract the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is + 2 1600, 1500, 1400, 1300, … common difference is -100

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.

Geometric Sequence Multiply by the same number each time (although it may appear as if you are dividing) This is called the common ratio and is always represented by multiplication. examples 1, 4, 16, 64, … common ratio is 4 400, 200, 100, 50, … common ratio is x 1/2 (dividing by 2 is the same as multiplying by 1/2)

Geometric Sequence 4, 8, 16, 32, 64, 128,… Common ratio: x 2 2000, 1000, 500, 250, 125, 62.5,… Common ratio: 𝐱 ½ 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 Start at 1, rule: x 2 Start at 1000, x 1/2 Start at 3, x 3 Start at 390,625, x 1/5 Start at 218,700, x 1/3 Start at 1, x 4 Start at 1, rule: +2 Start at 1000, -50 Start at 12, +6 Start at 81, -9 Start at 13, +5 Start at 20, -4

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06 SOL 6.17

Powers of 10 exponent base Ten to the 3rd power =10 x 10 x 10 = 1000

Powers of Base 10

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08 SOL 6.21, 6.22*

Look for patterns all around you

Square Numbers Numbers that can be represented by dots in a square array. 1st four square numbers are depicted below:

Perfect Square Numbers! Floor Tiles Perfect Square Numbers! 𝟏 𝟐 = 1 𝟐 𝟐 = 4 𝟑 𝟐 = 9 𝟒 𝟐 = 16 𝟓 𝟐 = 25

Triangular Numbers Numbers that can be represented by dots in a triangular array. 1st four triangular numbers are depicted below: 1 3 6 10 +2 +3 +4

1 , 3 http://collegian.csufresno.edu/2008/04/18/chingy-for-change-a-cause-on-pause-for-a-quick-game/ , 6 , 10

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Fibonacci Sequence http://www.fibonacci.name/

Fibonacci Sequence

1+1 =2 1+2 =3 2+3 =5 3+5 =8 5+8 =13 mat-cast.com

Fibonacci Sequence

The Fab 5 1, 1, 2, 3, 5, 8, 13, 21, 34 Perfect Square Multiply n*n 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 The Fab 5 Arithmetic + or – the common difference 2, 4, 6, 8, 10 Triangular Add one more each time 1, 3, 6, 10 Geometric X or / the common ratio 2, 4, 8, 16, 32 1, 10, 100, 1000 Fibonacci Add the last 2 to get the next 1, 1, 2, 3, 5, 8, 13, 21, 34 worksheet