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Arithmetic & Geometric Sequences Arithmetic & Geometric Sequences

Arithmetic & Geometric Sequences - PowerPoint Presentation

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Uploaded On 2018-09-21

Arithmetic & Geometric Sequences - PPT Presentation

4 3 2 1 0 In addition to level 30 and above and beyond what was taught in class  the student may Make connection with other concepts in math Make connection with other content areas ID: 673509

geometric sequence term arithmetic sequence geometric arithmetic term rule common write difference find explicit relationship student quantities formula sequences

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Slide1

Arithmetic & Geometric SequencesSlide2

4

3210In addition to level 3.0 and above and beyond what was taught in class,  the student may:· Make connection with other concepts in math· Make connection with other content areas.The student will build a function (linear and exponential) that models a relationship between two quantities. The primary focus will be on arithmetic and geometric sequences. - Linear and exponential functions can be constructed based off a graph, a description of a relationship and an input/output table. - Write explicit rule for a sequence. - Write recursive rule for a sequence.The student will be able to:- Determine if a sequence is arithmetic or geometric. - Use explicit rules to find a specified term (nth) in the sequence.  With help from theteacher, the student haspartial success with building a function that models a relationship between two quantities.Even with help, the student has no success understanding building functions to model relationship between two quantities.

Focus 7 Learning Goal –

(HS.F-BF.A.1, HS.F-BF.A.2, HS.F-LE.A.2, HS.F-IF.A.3)

=

Students will build a function (linear and exponential) that models a relationship between two quantities. The primary focus will be on arithmetic and geometric sequences.Slide3

Arithmetic Sequence

In an Arithmetic Sequence the difference between one term and the next term is a constant.We just add some value each time on to infinity.For example:1, 4, 7, 10, 13, 16, 19, 22, 25, …This sequence has a difference of 3 between each number.It’s rule is an = 3n – 2.Slide4

Arithmetic Sequence

In general, we can write an arithmetic sequence like this:a, a + d, a + 2d, a + 3d, …a is the first term.d is the difference between the terms (called the “common difference”)The rule is:xn = a + d(n-1)(We use “n-1” because d is not used on the 1st term.)Slide5

Arithmetic Sequence

For each sequence, if it is arithmetic, find the common difference.-3, -6, -9, -12, …1.1, 2.2, 3.3, 4.4, …41, 32, 23, 14, 5, …1, 2, 4, 8, 16, 32, …d = -3d = 1.1d = -9Not an arithmetic sequence. Slide6

Arithmetic Sequence

Write the explicit rule for the sequence19, 13, 7, 1, -5, … Start with the formula: xn = a + d(n-1)a is the first term = 19d is the common difference: -6The rule is:xn = 19 - 6(n-1)Find the 12th term of this sequence.Substitute 12 in for “n.”x12 = 19 - 6(12-1)

x

12

=

19

-

6

(11)

x

12

=

19

– 66

x

12

=

19

- 6

(12-1)

x

12

=

-47Slide7

Geometric Sequence

In a Geometric Sequence each term is found by multiplying the pervious term by a constant.For example:2, 4, 8, 16, 32, 64, 128, …The sequence has a factor of 2 between each number.It’s rule is xn = 2nSlide8

Geometric Sequence

In general we can write a geometric sequence like this:a, ar, ar2, ar3, …a is the first term r is the factor between the terms (called the “common ratio”).The rule is xn = ar(n-1)We use “n-1” because ar0 is the 1st term.Slide9

Geometric Sequence

For each sequence, if it is geometric, find the common ratio.2, 8, 32, 128, …1, 10, 100, 1000, …1, -1, 1, -1, …20, 16, 12, 8, 4, …r = 4r = 1.1r = -1Not a geometric sequence. Slide10

Geometric Sequence

Write the explicit rule for the sequence3, 6, 12, 24, 48, … Start with the formula: xn = ar(n-1)a is the first term = 3r is the common ratio: 2The rule is:xn = (3)(2)(n-1)(Order of operations states that we would take care of exponents before you multiply.)Find the 12th term of this sequence.Substitute 12 in for “n.”x12 = (3)

(2

)

(12-1

)

x

12

=

(3)

(2

)

(11)

x

12

=

(

3)

(2048)

x

12

=

6,144Slide11

Group Activity

Each group will receive a set of cards with sequences on them. Separate the cards into two columns: Arithmetic and Geometric.For each Arithmetic Sequence, find the common difference and write an Explicit Formula.For each Geometric Sequence, find the common ratio and write a Explicit Formula.Slide12

Explain the difference between an

Arithmetic and Geometric Sequence.