Sequences 5.2.

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Presentation transcript:

Sequences 5.2

Arithmetic Sequences Pg. 357 Numbers Words Continue each sequence. 1,3,5,7,__,__,... 1,1.5,2,__,__,__,.. Describe each sequence. Add __ to the previous term. Add ___ to the previous term.

Horseback Riding: The number of students who went on each horseback riding trip is show. Do the numbers represent the terms of an arithmetic sequence? Explain. Real-World Link Trip 1 2 3 4 5 Number of Students 15 16 18 21 25 ___________________________________________________________________________________________________________________________

Vocabulary arithmetic sequence - a list of numbers in which the next term is found by _______ the same number to the previous term. geometric sequence - a list of numbers in which the next term is found by ________ the previous term by the same number to get the next term.

Describe and Extend Sequences In an ___________, the terms can be whole numbers, fractions, or decimals. Examples on pg. 358

Write an Algebraic Expression In a _________, each term has a specific position within the sequence. Consider the sequence 2, 4, 6, 8… 2, 4, 6, 8, … ___ position 1st position ___ position __ position

the same number was added Arithmetic Sequences 2, 5, 8, 11, 14, . . . . +3 +3 +3 +3 n + 3 the same number was added common difference = 3

the same number was added 1, 8, 15, 22, 29, . . . . +7 +7 +7 +7 n + 7 the same number was added common difference = 7

multiplied by the same number Geometric Sequences 2, 6, 18, 54, . . . . •3 •3 •3 3n multiplied by the same number common ratio = 3

multiplied by the same number Geometric Sequences 1, 5, 25, 125, . . . . •5 •5 •5 5n multiplied by the same number common ratio = 5

Find the 7th term in the sequence. 89, 86, 83, 80. . . 77 74 71 n-3 -3 -3 -3 2, 4, 8, 16. . . 32 64 128 2n •2 •2 •2

Arithmetic or Geometric Sequence Arithmetic or Geometric Sequence? Then find the next 3 terms & the algebraic expression. 7, 12, 17, 22. . . 27 32 37 +5 n+5 +5 +5 64, 32, 16, 8. . . 4 2 1 •0.5 •0.5 •0.5 0.5n ÷2 ÷2 ÷2

Classwork Practice

Classwork Practice Identify each sequence as arithmetic or geometric, then write a variable expression to describe it. 1. 2, 4, 6, 8, .... 2. 6, 12, 24, 48, .... 3. 4, 4, 4, 4, 4, .... 4. 4, 7, 10, 13, .... 5. 1, 7, 13, 19, ....

6. 2, 4, 8, 16, .... 7. 11, 22, 33, 44, .... 8. 24, 12, 6, 3, .... 9. 21, 18, 15, 12, .... 10. 2, 8, 32, 128, ....