Download Sequences

Sequences
Objectives:
…to describe, extend, or find a missing element of a pattern
Assessment Anchor:
7.D.1.1 – Recognize, reproduce, extend and/or describe patterns,
sequences and relationships.
Vocabulary alert!!
SEQUENCE – a set of numbers that follow a pattern
ARITHMETIC SEQUENCE – a sequence where each term is found by
adding or subtracting the same number to
the previous term
GEOMETRIC SEQUENCE – a sequence where each term is found by
multiplying or dividing the previous term by
the same number
NOTES
Finding the pattern:
1. Consider a common difference (what’s being added or subtracted)
2. Consider a common ratio (what’s being multiplied or divided)
3. Consider an alternating pattern
Write a rule for the sequence:
TEMPLATE #1 (for arithmetic and geometric)
“Start with ___, then _________________ repeatedly.”
TEMPLATE #2 (for alternating patterns)
“Start with ___, then alternate between _____________________.”
Sequences
EXAMPLES
Sequence #1:
3, 7, 11, 15, 19, ___, ___, ___, …
(common difference)
+4 +4
RULE:
+4
“Start with 3, then add 4 repeatedly.”
Sequence #2:
4, 8, 16, 32, 64, ___, ___, ___, ___, …
4, 8, 16, 32, 64, 128, 256, 512, …
Geometric sequence:
(common ratio)
RULE:
+4
3, 7, 11, 15, 19, 23, 27, 31, …
Arithmetic sequence:
×2
×2
×2
×2
“Start with 4, then multiply by 2 repeatedly.”
Sequence #3:
1.3, 2.9, 4.5, 6.1, ___, ___, ___, ___, …
(common difference)?
Arithmetic? or Geometric?
1.3, 2.9, 4.5, 6.1, ____, ____, ____, …
(common ratio)?
RULE:
___________________________________________________
Sequence #4:
48, 24, 12, 6, ___, ___, ___, …
(common difference)?
Arithmetic? or Geometric?
48, 24, 12, 6, ____, ____, ____, …
(common ratio)?
RULE:
___________________________________________________
“Don’t just THINK about what’s happening…
find out, and write it down!”
Sequences
MORE EXAMPLES
Sequence #5:
18, 10, 20, 12, 24, ___, ___, ___, …
(difference)?
Arithmetic? or Geometric?
18, 10, 20, 12, 24, ____, ____, ____, …
(ratio)?
RULE: ___________________________________________________________
Sequence #6:
3, 12, 13, 52, 53, ___, ___, ___, …
(difference)?
Arithmetic? or Geometric?
3, 12, 13, 52, 53, _____, _____, _____, …
(ratio)?
RULE: ___________________________________________________________
Sequence #7:
21.5, 21, 10.5, 10, 5, ___, ___, ___,…
(difference)?
Arithmetic? or Geometric?
21.5, 21, 10.5, 10, 5, ____, ____, ____, …
(ratio)?
RULE: ___________________________________________________________
Sequence #8:
18, 68, 34, 84, 50, ___, ___, ___, …
(difference)?
Arithmetic? or Geometric?
18, 68, 34, 84, 50, _____, _____, _____, …
(ratio)?
RULE: ___________________________________________________________