Sequences 5 2 Arithmetic Sequences Pg 357 Numbers

Sequences 5. 2

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

Real-World Link 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. Trip Number of Students 1 15 2 16 3 18 4 21 5 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… 1 st position ___ position 2, 4, 6, 8, … __ position ___ position

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

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

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

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

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

Arithmetic or Geometric Sequence? Then find the next 3 terms & the algebraic expression. 7, 12, 17, 22. . . 27 32 37 +5 +5 n+5 +5 64, 32, 16, 8. . . 4 • 0. 5 ÷ 2 ÷ 2 2 0. 5 n 1

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, 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, . .