2.3 number sequences
Post on 09-Feb-2016
56 Views
Preview:
DESCRIPTION
TRANSCRIPT
Square/Rectangular NumbersTriangular NumbersHW: 2.3/1-5
What are we going to learn today, Mrs Krause?
• You are going to learn about number sequences.• Square, rectangular & triangular
• how to find and extend number sequences and patterns
• change relationships in patterns from words to formula using letters and symbols.
2 4 6 8 10 _ _ _1)
1 3 5 7 9 _ _ _2)
25 50 75 100 125 _ _ _3)
1 4 9 16 25 _ _ _4)
5 9 13 17 21 _ _ _5)
8 14 20 26 32 _ _ _6)
1 3 6 10 15 _ _ _8)
12 14 16
11 13 15
150 175 200
36 49 64
38 44 50
25 29 33
21 28 36
Perfect Squares
Triangular Numbers
Even Numbers
OddNumbers
Multiples 25
Add 4
Add 6
15 24 35 48 63 _ _ _7) 80 99 120 Add next odd numberRectangular
Numbers
Add next integer
n 1 2 3 4 5 6 7 8
Square NumbersTerm Value
1st 1
2nd 4
3rd 9
4th 16
Square Numbers
Term Value5th 25 or 5 * 5
6th 36 or 6 * 6
7th 49 or 7 * 7
8th 64 or 8 * 8
nth n * n or n2
The sequence 3, 8, 15, 24, . . . is a rectangular number pattern. How many squares are there in the 50th rectangular array?
Rectangular Numbers
STEPS to write the rule for a Rectangular Sequence(If no drawings are given, consider drawing the rectangles to
represent each term in the sequence)Step 1: write in the base and height of each rectangleStep 2: write a linear sequence rule for the base then the heightStep 3: Area = b*h; use this to write the rule for the entire rectangular sequence
*Base 3, 4, 5, 6, … (n+2)*Height 1, 2, 3, 4, … (n)
Rectangular sequence = base * height = (n+2)(n)
1432
3 4 56
Add the next odd integer: +5, 7, 9,..
Use the Steps to writing the rule for a Rectangular Sequence to find the rule for the following sequence
2, 6, 12, 20,..
n 1 2 3 4 5 6 … n …
value 2 6 12 20
Step 1: write in the base and height of each rectangle
1*2 2*3 3*4 4*5 5*6 6*7
Step 2: write a linear sequence rule for the base then the heightBase = 1, 2, 3, 4, … nHeight = 2, 3, 4, 5, … n+1
Step 3: Area = b*h; use this to write the rule for the entire rectangular sequence
nth term rule n(n+1)
30 42 n(n+1)
STEPS to write the rule for a Triangular SequenceStep 1: double each number in the value row
create rectangular numbersStep 2: write in the base and height of each rectangleStep 3: write a linear sequence rule for the base then the heightStep 4: Area = b*h; use this to write the rule for the entire rectangular sequenceStep 5: undo the double in Step 1 by dividing the rectangular rule
by 2.
1 3 6 10
n 1 2 3 4 5 nthvalue 1 3 6 10 15 … …2*value 2 6 12 20 30 1*2 2*3 3*4 4*5 5*6
Step 1: double each number in the value row create rectangular numbers
Step 2: write in the base and height of each rectangle
Step 3: write a linear sequence rule for the base then the heightStep 4: Area = b*h; use this to write the rule for the entire rectangular sequenceStep 5: undo the double in Step 1 by dividing the rectangular rule by 2.
1
3
6
10
Find the next 5 and describe the pattern
Triangular Numbers
15, 21, 28, 36, 45…….n ?
1st 1 * 2 = 2
2nd 2 * 3 = 6
3rd 3 * 4 = 12
4th 4 * 5 = 20
Does this help?Can you see a pattern yet?
Try this to help write the nth term.
(4 * 5) = 20 = 10 2 2
So what about the nth number in the sequence?
4 * 5 = 20
This is the 4th in the sequence
n (n +1)
2
15 24 35 48 63 7)
2 4 6 8 101)
1 3 5 7 92)
25 50 75 100 1253)
1 4 9 16 254)
5 9 13 17 215)
8 14 20 26 326)
1 3 6 10 15 8)
2n
(2n) - 1
25n
(4n) + 1
(6n) + 2
n2
nth term1 2 3 4 5
(n+2)(n+4)
A RuleWe can make a "Rule" so we can calculate any triangular number.
First, rearrange the dots (and give each pattern a number n), like this:
Then double the number of dots, and form them into a rectangle:
The rectangles are n high and n+1 wide (and remember we doubled the dots):
Rule: n(n+1) 2
Example: the 5th Triangular Number is
5(5+1) = 15 2
Example: the 60th Triangular Number is
60(60+1) = 18302
Linear Sequences: add/subtract the common difference
Square/ rectangular Sequences: add the next even/odd integer
Triangular Sequences: add the next integer
How to identify the type of sequence
So what did we learn today?
• about number sequences. • especially about square , rectangular and triangular numbers.
• how to find and extend number sequences and patterns.
9
9+1=10
9x10 = 90Take half.
Each Triangle has 45.
459 n
top related