Download 6.17-Interactive

The student will identify and extend
geometric and arithmetic
sequences.
Pg
6.17 practice
6.17 Vocabulary
POWERS OF TEN (just count the zeroes and that is your power)
101 = 10
103 = 1,000
105
Numerical patterns may include linear and exponential growth, perfect squares,
triangular and other polygonal numbers, or Fibonacci numbers.
• Arithmetic and Geometric sequences are types of numerical patterns.
= __________
Triangular Numbers, just add a row to the bottom. What is the number in the 8th position?
1
2
3
1
2
1ST term
1
2
3
4
5
1
2
3
4
2ND term
3
6
3RD term
4TH term
10
15
6TH
7TH
Perfect squares! What is the number in the 6th position?
22
32
42
pg-
Arithmetic sequence,
determine the difference, called the common difference, between each succeeding
number in order to determine what is ADDED to each previous number to obtain
the next number. Sample numerical patterns are
6, 9, 12, 15, 18, …;
and 5, 7, 9, 11, 13, ….
8TH
Geometric number patterns, determine what each number is MULTIPLIED by to
obtain the next number in the geometric sequence. This multiplier is called the
common ratio. Sample geometric number patterns include
2, 4, 8, 16, 32, …; 1, 5, 25, 125, 625, …;
and 80, 20, 5, 1.25, …
***Geometric patterns may involve shape, size, angles, transformations of shapes,
and growth.
Common ratio
The ratio used to determine what each number is multiplied by
in order to obtain the next number in the geometric sequence
1ST term
4
2ND term
9
3RD term
4TH
16
____
5TH
_____
6TH
______
Fibonacci Sequence!
Each number is the sum of the previous two numbers. Name the 12th term.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34,
____, ____
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th
12th
Find the common difference or
x
y
common ratio and name as an
1
3
arithmetic or geometric pattern
64, 16,
4,
1
____________
2
3
5
7
35, 40 _____________
Triangular number- A triangular number can be represented geometrically as a
certain number of dots arranged in a triangle, with one dot in the first (top) row
and each row added having one more dot that the row above it. To find the next
triangular number, a new row is added to an existing triangle. The first row has 1
dot, the second row 2 dots, the third row 3 dots and so on. So add 1 + 2+ 3= 6 or
just count all the dots.
Square Number- A square number can be represented geometrically as the
number of dots in a square array. Square numbers are perfect squares and are the
numbers that result from multiplying any whole number by itself (e.g., 36 = 6  6).
Powers of 10 - 1, 10, 100, 1,000, 10,000
(just count the zeros
and that is your power)
Consecutive- Following one after the other in order.
rule?___________
25, 30,
Common difference
The difference between each succeeding
number in order to determine what is added to each previous number to obtain
the next number in a arithmetic pattern.
What is the tenth shape?
• Strategies to recognize and describe the differences between terms in numerical
patterns include, but are not limited to, examining the change between
consecutive terms, and finding common factors. An example is the pattern
1, 2, 4, 7, 11, 16,…