Download arithmetic sequence

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…
1st position
___ position
2, 4, 6, 8, …
__ position
___ position
Arithmetic Sequences
2, 5, 8, 11, 14, . . . .
+3
+3
+3
+3
n+3
the same number was added
common difference = 3
1, 8, 15, 22, 29, . . . .
+7
+7
+7
+7
n+7
the same number was added
common difference = 7
Geometric Sequences
2, 6, 18, 54, . . . .
•3
•3
•3
3n
multiplied by the same number
common ratio = 3
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
-3
-3
-3
n-3
2, 4, 8, 16. . . 32 64 128
•2
•2
•2
2n
Arithmetic or Geometric Sequence?
Then find the next 3 terms
& the algebraic expression.
7, 12, 17, 22. . . 27 32 37
+5
+5
+5
n+5
64, 32, 16, 8. . . 4
•0.5 •0.5 •0.5
÷2 ÷2 ÷2
2
0.5n
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, ....
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,
....