# U2.9: Arithmetic and Geometric Sequences

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Arithmetic and geometric sequences

### Text of U2.9: Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

Arithmetic and Geometric SequencesU2.9.1 3/20/15

Patterns in Nature

Famous Fibonacci Sequence

Wowsers! Cool Nature!

Fibonachos

Numerical patterns are called sequencesWarm-Up 2.9.1Describe the pattern and determine the next number in the list1, 3, 5, 7, 13, 18, 23, 28, 7, 4, 1, -2, -5, -22, -15, -8, -1, 1, 3, 9, 27, 256, 64, 16, 4, 4, 8/3, 16/9, 32/81, 1/2, -1/4, 1/8, -1/16,

DefinitionsArithmetic Sequence: is one in which each member of the sequence has a constant factor added or subtracted to get the next member. Ex.: 2,4,6,8,12,14

Geometric Sequence: is one in which each member of the sequence is multiplied or divided by a constant factor to get the next number.Ex.: 2,6,18,54,162,486,1458

Who is Who

Arithmetic Sequence: basics to know Common Difference : is the constant difference between the numbers of the sequence is the number we added or subtracted

Explicit Formula or rule: Is the formula used to find the nth term of a sequence nth term: is the number of terms in the sequence

Recursive formula or rule: a formula used to find the next term of a sequence when the previous term is known

Arithmetic Sequences are linear functions!!!

http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html

Mathisfun.com

Arithmetic Recursion Formula:

Ex.:

Recursion= Iteration

Kuta Software

Yeah!!!!

Geometric Sequence: basics to knowConstant Ratio: the constant number we multiplied or divided by to get the next number.

Explicit formula or rule: a formula used to find the nth term of the sequence

nth term: is the number of terms in the sequence

Recursive formula or rule: Recursive formula or rule: a formula used to find the next term of a sequence when the previous term is known

Geometric Sequences are exponential functions!!!

http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

Guided Practice

The area of a square A=bxl=5x5=25

__ , __ , __ , 27 , __ , __ , 1This can only happens if we are dividing each term by 3 (common ratio) so to retrace we multiplied by 3: 27x3=81, 81x3=243, 243x3=729

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