Upload File

1, 3, 5, 7, 9, … + 2 termnumberspattern of numbers the n-order for the pattern of odd numbers is...

  • Home
  • Documents
  • 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?
11

Upload: taryn-taft

Post on 31-Mar-2015

215 views

Category:

Documents


0 download

Report

Tags:

TRANSCRIPT

Page 1: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?
Page 2: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1 , 3 , 5 , 7 , 9 , …+ 2

+ 2

+ 2

+ 2Term Numbers Pattern of

Numbers

The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers

1

2

3

4

n

1

3

5

7

?

2 (1) – 1 = 1 2 (2) – 1 = 3

2 (3) – 1 = 5

2 (4) – 1 = 7

2 (n) – 1 = 2n – 1

Page 3: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

2 , 4 , 6 , 8 , 10 , …+

2+ 2

+ 2

+ 2Term Numbers Pattern of

Numbers

The n-order for the pattern of even numbers is 2n, for n is natural numbers

1

2

3

4

n

2

4

6

8

?

2 (1) = 2 2 (2) = 4

2 (3) = 6

2 (4) = 8

2 (n) = 2n

Page 4: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1 x2

2 x 3 3 x 4

2 6 12 …

… x …

…

Term Numbers Pattern of Numbers

nth term = n2 + n

1

23

…

n

2

612

…

?

1 ( 1 + 1) = 2

…

2 ( 2 + 1) = 6

3 ( 3 + 1) = 12

n ( n + 1) = n2 + n

Page 5: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1 3 6 10 15 …

…

Term Numbers Pattern of Numbers 1 1 1 2

12 2

2 2 1 63

2 2

3 3 1 126

2 2

12

n n

1

2

3

…

n

1

3

6

…

?

…

Page 6: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1 x1

2 x 2

3 x 3

4 x 4

5 x 5 …

…

…

1 4 9 16 25

nth term = n2

Term Numbers Pattern of Numbers 1

23

…

n

1

49

…

?

(1)2 = 1(2)2 = 4(3)2 = 9

(n)2 = n2

…

Page 7: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

Term Numbers Pattern of Numbers

11 1

1 2 11 3 3 1

1 4 6 4 1

1248

16

1

23

…

n

1 = 20

…

?

2 = 21

4 = 22

21 – 1

22– 1

23 – 1

2n – 1

…

nth term = 2n – 1

Page 8: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1. Find the sum of a. 1 + 3 + 5 + 7 + 9 + 11!b. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 !

Solution

The pattern of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 is the first of 10 0dd numbers, so n = 10.

10 term

Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = n2 =

102 = 100

10 term

b.

a. The pattern of 1 + 3 + 5 + 7 + 9 + 11 is the first of 6 0dd numbers, so n =

6.6 termTherefor

e,1 + 3 + 5 + 7 + 9 + 11 = n2 = 62 = 36

6 term

Page 9: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

2. Find the line of the pattern of Pascal Triangle numbers if the sum of the lines is 256!Solution

256 = 2n – 1

28 = 2n – 1

8 = n – 1 n = 8 + 1 n = 9

Hence, the pattern of Pascal Triangle numbers where the sum is 256 is the 9th lines

3. Find the pattern of rectangle numbers until the 9th term!Solution Term Pattern of

NumbersNumbers

1 1 ( 1 + 1) 2

2 2 ( 2 + 1) 6

3 3 ( 3 + 1) 12

4 ... …

5 … …

6 … …

7 … …

8 … …

9 … …

2, 6, 12, 20, 30, 42, 56, 72, 90

Page 10: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1. Find the next three figures from the following figures!

2. Find a. The 20th order of the pattern of square numbers;b. The 28th order of the pattern of square numbers;c. The 30th order of the pattern of square numbers!

3. Copy the figure of Pascal Triangle and then continue until the 10th line!

4. Find the sum of following Pascal Triangle numbers linesa. The 8th lines;b. The 10th lines!

5. Find how many terms of the first even numbers, if the sum is 156!

Page 11: 1, 3, 5, 7, 9, … + 2 TermNumbersPattern of Numbers The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers 1 2 3 4 n 1 3 5 7 ?

1. Pattern of odd numbers

The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers

2. Pattern of even numbers

The n-order for the pattern of even numbers is 2n, for n is natural numbers

4. Pattern of triangle numbers

5. Pattern of square numbers

6. Pattern of Pascal triangle numbers

12

n n

nth term = n2

nth term = 2n – 1

3. Pattern of rectangle numbers

nth term = n2 + n


arXiv:math.CO/0507163 v1 7 Jul 2005apost/papers/permutohedron_full.pdfEulerian numbers, the Catalan numbers, the binomial coefficients, the factorials, the number (n + 1)n−1 of trees,

§3 Dynamic Programming Use a table instead of recursion 1. Fibonacci Numbers: F(N) = F(N – 1) + F(N – 2) int Fib( int N ) { if ( N

sum of the first n numbers

UNITED STATES POST OFFICE BROOKLYN 1, N. Y....UNITED STATES POST OFFICE Brooklyn 1, N. Y. POSTAL ZONE NUMBERS-BROOKLYN, N. Y. Special Instructions: Where no street numbers are shown,

n Dimensional Hyperbolic Numbers

INTEGER NUMBERS€¦ · INTEGER NUMBERS Integer numbers : Positive numbers, negative numbers and zero. We use the number line to represent numbers Z N 0, 1, 2, 3, -1, -2, -3,

GCD of n Numbers

U N I T Whole Numbers - MS. TRACY BEHL 4Abehlblog.weebly.com/.../mms4_textbook_unit2_wholenumbers.pdf · 2019. 4. 26. · U N I T Whole Numbers Goals •recognize and read numbers

T N 3098 Numbers 1 50 on Children

1 EXPLORATION: Classifying Numbers€¦ · 1 EXPLORATION: Classifying Numbers Complex Numbers Real Numbers Imaginary Numbers Rational Numbers Irrational Numbers Integers Whole Numbers

What if n=1??? - cs.umd.edu · numbers and all numbers between 1 and N will come through the feed ... 1 k cij aik bkj. Run-Time Improvement? Using the brute force algorithms that

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 17 Index Numbers n Price Relatives n Aggregate Price Indexes n Computing an Aggregate

Algorithms Growth of Functions. Some Notation NNatural numbers RReal numbers N + Positive natural numbers R + Positive real numbers R * Non-negative real

SURREAL NUMBERS AND THE N-QUEENS GAME Hassan A Noon.liacs.leidenuniv.nl/~kosterswa/nqueens/papers/noon2002.pdf · 1 - Surreal Numbers Dedekind constructed real numbers by partitioning

Homotopy Theory and · Homotopy-calculus 1 Free homotopy types Xn i=1 i = n(n + 1)/2 Xn i=1 i = n(n + 1)/2 i 2 N – natural i 2 Z – integers numbers e.g. 1 + . . . + 10 = 55 X

THE INTRODUCTION OF COMPLEX NUMBERS* John N. Crossleysms.math.nus.edu.sg/smsmedley/vol-08-1/the... · THE INTRODUCTION OF COMPLEX NUMBERS* John N. Crossley Monash University, Melbourne,

EULER–FROBENIUS NUMBERS AND ROUNDINGweb.math.rochester.edu/misc/ojac/vol8/74.pdfThe Eulerian numbers An,k,1 ˘ An,k¯1,0 for small n. The row sums are n!. that these polynomials

New magic numbers N = 32, 34 - University of Adelaide · New magic numbers N = 32, 34 1 Study the nuclear shell evolu1on at N = 32, 34 by direct mass measurements of neutron-rich

Squares and Square Roots - Cloudinary · (n + 1) 2 – n = (n 2 + 2n + 1) – n = 2n + 1. We find that between n2 and (n + 1) 2 there are 2 n numbers which is 1 less than the difference

1 1 Slide Chapter 6 Simulation n Advantages and Disadvantages of Using Simulation n Modeling n Random Variables and Pseudo-Random Numbers n Time Increments

Congruences for Franel Numbers - Nanjing Universitymaths.nju.edu.cn/~zwsun/CongFranel.pdf · Franel numbers In 1894 J. Franel introduced the Franel numbers f n = Xn k=0 n k 3 (n =

THE NATURAL NUMBERS N 0, 1, 2, 3, 4.... 1.- EVOLUTION OF NUMBERS »The numbers appeared due to the necessity of counting. »Primitive societies created

REPRESENTATION NUMBERS BY SUMS OF QUADRATIC FORMS X CX2 CX ... · representation numbers of sums of quadratic forms 279 w3;3 2;3.n/ d 1 240 ˙3. n 2 / 1 240 ˙3. n 3 /c 1 167280 ˙7.n/c

Permutation and Combination SRI HARSHA. Basic Information Factorial: The continuedProduct of first n natural numbers is called n! n! = 1*2*3*4*…… (n–1)

Dialogue on n colored numbers

Concise UNIMARC Classification Format one of the letters A-Z n Not Applicable /3 Use of Auxiliary Table Numbers as Main Numbers a Auxiliary Table Numbers Used as Main Numbers n Not

“Named” numbres - University of Washingtonfaculty.washington.edu/moishe/hanoi-2011... · 4 1;1;2;3;5;8;13;::: Fibonacci numbers. 5 n k binomials. 6 1 n+1 2n n the Catalan numbers

1. General Project Description - Houston · 1121 Walker, Houston, TX July 31, 2015 Page 1 1. General Project Description Photo numbers 1‐9 Drawing numbers N/A The Melrose Building

4.2 Irrational Numbers - Mrs. N. Gill€¦ · 4.2 Irrational Numbers November-05-13 9:03 AM 4.2 Irrational Numbers Page 1 . 4.2 Irrational Numbers Page 2 . Created Date: 11/5/2013

mth428h14.files.wordpress.comChapter 1 Complex Numbers and Functions 1.1 De nition We have learned several systems of numbers. They are 1. N = f1;2;3;:::g, natural numbers. 2. Z =

1 1 Slide Chapter 13 Simulation n Advantages and Disadvantages of Using Simulation n Modeling n Random Variables and Pseudo-Random Numbers n Time Increments

Computer Programming C++ (66111) average for N input numbers ... •Sum •N 37 Flowchart example 3 ... while reading the N numbers. Program design

Tri Lai - math.unl.edutlai3/Catalan Objects.pdf · Catalan Numbers C n = 1 n+1 2n n The number offull binary treewith2n + 1vertices (i.e., n internal vertices). The number oftriangulationsof

An Introduction to the Narayana Numbers · The Narayana numbers N(n;k) for 1 k n form a triangular array of positive integers, introduced in 1915-1916 by the combinatorialist P. A

Rational Numbers & Equations - Centennial School …...M08.A-N.1.1.4: Use rational approximations of irrational numbers to compare and order irrational numbers. 2.2, 4.6 M08.A-N.1.1.5: