Number Patterns and Sequences

Introduction to Number Patterns

A number pattern means an arrangement of numbers that has a regular form or a number that is composed of several other numbers that form a pattern. And number patterns also have many types or types. On this occasion, we will study it together.

Types of Number Patterns

1. Odd Number Patterns Odd number patterns are number patterns formed from odd numbers. Meanwhile, the definition of an odd number itself means a natural number that is not divisible by two or multiples.odd number patterns are: 1, 3, 5, 7, 9, . . . .Odd number pattern image: Odd Number Pattern Formula1 , 3 , 5 , 7 , . . . , n , then the formula for the nth odd number pattern is:Un = 2n – 1 Example :1 , 3 , 5 , 7 , . . . , to 10What is the pattern for the 10th odd number?Answer :Un = 2n – 1U10 = 2 . 10 – 1= 20 – 1 = 192. Even Number Patterns Even number patterns are number patterns formed from even numbers. Even numbers are natural numbers, namely natural numbers that are divisible by two or multiples thereof. The pattern of even numbers is: 2, 4, 6, 8, . . .Draw an even number pattern: Even number pattern formula2 , 4 , 6 , 8 , . . . . , n then the formula for the pattern of the nth even number is: Un = 2n Example :2 , 4 , 6 , 8 , . . . to 10. What is the pattern of even numbers to 10?answer :Un = 2nU10 = 2 x 10= 203. Square number pattern Square number pattern, namely a sequence of numbers that form a square pattern. The square number pattern is 1, 4, 9, 16, 25, . . .Square number pattern image: Square number pattern formula1 , 4 , 9 , 16 , 25 , 36 , . . . , n maka rumus untuk mencari pola bilangan persegi ke n adalah :Un = n2From a sequence of numbers 1, 2, 9, 16, 25, 36, . . . , to 10 . What is the 10th number pattern in the square number pattern?Answer :Un = n2U10 = 102 = 1004. Rectangular Number Pattern A rectangular number pattern is a sequence of numbers that form a rectangular pattern. The rectangle pattern is 2 , 6 , 12 , 20 , 30 , . . .Rectangular Number Pattern Image: Rectangular number pattern formula2 , 6 , 12 , 20 , 30 , . . . n, then the formula for the nth rectangular number pattern is:Un = n . n+1 Example :From a sequence of numbers 2, 6, 12, 20, 30, . . . , to 10 . What is the pattern for the 10th square number?Answer :Un = n . n+ 1U10 = 10 . 10+1= 10 . 11= 1105. Triangular Number Patterns A triangular number pattern is a sequence of numbers that form a triangular number pattern. The triangle number pattern is: 1, 3, 6, 10, 15, . . .Image of triangular number pattern: Triangular Number Pattern Formula:1 , 3 , 6 , 10 , 15 , 21 , 28 , 36 , . . . , to n . So the formula for the nth triangular number pattern is: Un = 1 / 2 n ( n + 1 ) Problems example :From a sequence of numbers 1, 3, 6, 10, 15, 21, 28, 36, . . . , to 10 . What is the 10th triangle number pattern?Answer :Un = 1/2 n ( n + 1 )U 10 = 1/2 .10 ( 10 + 1 )= 5 ( 11 ) = 556. FIBONACCI Number Pattern The Fibonacci number pattern is a number where each term is the sum of the two terms in front of it. Fibonacci number pattern:1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 56 , . . .2 , 2 , 4 , 6 , 10 , 16 , 26 , 42 , . . ..That is the basic explanation of number patterns in mathematics . In essence, a number pattern is a form of number sequence. When studied carefully, each pattern has its own structure and use, especially for understanding arithmetic and geometric series. I hope this is helpful.