P ATTERNS AND S EQUENCES SOL 6.17 BY K WOODARD AND K NORMAN

A RITHMETIC S EQUENCE Add or Subtract the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is , 1500, 1400, 1300, … common difference is -100

A RITHMETIC S EQUENCES 4, 7, 10, 13,… Common difference: , 24, 21, 18,… Common difference: - 3 5, 20, 35, 50,… Common difference: + 15

A RITHMETIC S EQUENCES ARE L INEAR P ATTERNS When you graph the pattern it makes a line Linear It goes up or down gradually.

G EOMETRIC S EQUENCE 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)

G EOMETRIC S EQUENCE

G EOMETRIC S EQUENCES ARE E XPONENTIAL P ATTERNS When you graph the pattern it makes a steep curve Exponent ial It goes up or down fast!

M AKE 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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P OWERS OF 10 Ten to the 3 rd power =10 x 10 x 10 = 1000 base exponent

P OWERS OF B ASE 10

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08 SOL 6.21, 6.22*

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

F LOOR T ILES Perfect Square Numbers!

T RIANGULAR N UMBERS Numbers that can be represented by dots in a triangular array. 1st four triangular numbers are depicted below:

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F IBONACCI S EQUENCE

F IBONACCI S EQUENCE

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F IBONACCI S EQUENCE

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