8 Macam-macam Pola Bilangan beserta Contoh Soal dan Jawabannya
8 Macam-macam Pola Bilangan beserta Contoh Soal dan Jawabannya – Understanding the various number patterns can be said to be quite useful for everyday life.
For example, you are a bookseller. On the first day sold 7 pieces. Furthermore, on the second day, 14 books were sold, and until the third day, 28 books were sold. From here, you can see the pattern, which is multiplied by two.
After all, number patterns are still basic mathematics. The type of question is almost always a matter of several tests. Starting from the CPNS entrance test, job selection, and much more. Let’s dig in together!
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Daftar Isi
Before starting to discuss the various number patterns, maybe some here still don’t know what they mean. So basically, in mathematics, there is an arrangement of numbers that can form a certain pattern.
There are odd-even forms, arithmetic, geometric series, and many more. The pattern means a fixed form, while numbers can mean units of numbers or numbers. From here, do you understand what a number pattern is?
Broadly speaking, a number pattern is an arrangement of numbers that can form a certain pattern. If you want to determine a certain arrangement of numbers that you don’t know, you can use a formula.
Macam-macam Pola Bilangan beserta Contoh Soal dan Jawabannya
After you know what a number pattern is, of course, there is other information that is no less important.
This time about various number patterns. Each number pattern will be explained below with examples of questions and answers:
1. Odd Number Pattern
The odd number pattern itself is the arrangement of numbers starting from 1 to infinity. Because of the odd number, the numbers referred to here are certainly only the odd ones.
Of course, you know what odd numbers are, right? Starting from 1,3,5,7, and so on until infinity is called the odd number pattern. Then how to find patterns of odd numbers? You can use the formula, namely Un= 2n -1.
Problems example:
To better understand one of the various number patterns on this one, maybe you should apply it to the problem. More or less examples of odd number patterns are as follows:
Determine the 9th odd number, using the odd number pattern calculation pattern, it will be
9th number = U9
Un = 2n – 1
U9 = 2(9) -1
U9s = 17
From these calculations, the result is obtained if the 9th odd number is 17.
2. Even Number Pattern
The following types of number patterns are even number patterns. If the number pattern is even, of course, it is the arrangement of numbers consisting of only even numbers.
Usually, the numbers in question can be divided by 2. The pattern of even numbers starts from 2,4,6,8 and so on.
Similar to one of the previous types of number patterns, the even number pattern also has its formula, namely Un = 2n, making it easier for everyone to calculate.
Problems example:
Still, want to know more about how the even number pattern is calculated? If there is a formula, it should be easier. Please just look at the examples of the even calculation pattern questions and the following answers
Determine the 9th even number. By using the even number pattern, you can use the formula, namely
9th number = U9
Un = 2n
U9 = 2(9)
U9s = 18
So, from these calculations, the result is obtained if the 9th even number is 18.
3. Square Numbers Pattern
There is another one of many other number patterns. This time it’s a square number pattern. From the name alone, it is known that the pattern of square numbers will form a flat shape, namely a square.
A square number pattern is an arrangement of numbers that can form a square shape.
The arrangement of numbers on a square number pattern to be formed by square numbers. For example, the square number pattern itself is 1,4,9,16, and so on.
It’s still the same as the various number patterns before. The square number pattern is also equipped with a formula to make calculations easier. The formula for the square number pattern is Un = n2 (squared)
Problems example:
Understanding the square number pattern is very easy. You only need to apply to the problem. Then using the available formula, the number pattern in question will be immediately easy to find out
For example, there is a question, what is the number of the 10th square? By using the formula, calculations can be obtained
The 10th number = U10
Un = n2
U10 = 102
U10 = 100
Thus, the result is obtained if the number of the 10th square is 100.
4. Arithmetic Number Pattern
One of the following types of number patterns is the arithmetic number pattern. This arithmetic number pattern has a fixed difference between the two terms.
In addition, the added numbers are always the same, namely 8, 16, 24, and so on. So a = 8 and b = 8.
Another example of an arithmetic number pattern is 1, 5, 9, 13, 17, 21, and so on. The difference between the 2nd and 1st numbers is 5-1=4.
While the 3rd and 2nd numbers are 9-5 = 4, meaning that the difference is always the same.
The formula for one of these number patterns is somewhat different from the others. The arithmetic number pattern formula can be calculated using the formula Un = a + (n-1) b with an explanation:
a = the first term of the number sequence
b = difference
n = order of the nth number
Problems example:
The formula is indeed a bit longer than before. However, the calculation is not that complicated. To understand it better, see the example question below.
For example, the problem is that you know the sequence of numbers 4,10,16, 22, 28, … then determine the 30th term
To answer this question, you must first make sure which are a and b so that:
a = 4
b = 6
Un = a + (n-1) b
U30 = 4 + (30 – 1) 6
U30 = 4 + 29 x 6
U30 = 4 + 174
U30 = 178
From the calculation above, it can be seen that the 30th term is 178.
5. Geometry Number Pattern
One of the various number patterns is the geometric number pattern. This geometric series number pattern has a fixed ratio between the two terms. An example of a geometric number pattern
are 2, 6, 18, 54, and so on. Meanwhile for the formula itself, namely Un = arn – 1 with the description:
a = the first term of the number sequence
r: ratio
n: the order of the nth numbers
Problems example:
To better understand one of these various number patterns, of course, you need an example problem. Examples of the easiest questions like:
The following is a geometric sequence 2, 8, 32,… so please determine the first term, the formula for the nth term and U5
a. Find the first term and its ratio
From the number pattern sequence, the first term is 2. While the ratio or r is 8/2=32/8=4
b. Looking for the nth Tribe
Un = a.r^ (n-1)
Un = 2.4^ (n-1)
c. Looking for U5
Un = 2.4^ (n-1)
Un = 2.4^ (5-1)
U5 = 2.4^4
U5 = 2.256
U5 = 512
From the calculation above, it can be seen that the answers to the examples of geometric number patterns are easy, right?
6. Rectangle Number Pattern
Want to know other kinds of number patterns? This time there is still such a thing as a rectangular number pattern. A rectangular number pattern is an arrangement of numbers that forms a rectangular shape.
Meanwhile, example of the rectangular number pattern itself is 2, 16, 12, and so on. The rectangular number pattern formula is Un = n(n+1).
Problems example:
Indeed, the thing that most make a person understand about the various number patterns is to directly look at the examples of the problems.
For example, when you want to calculate a rectangular number pattern. For that, try to look at the following examples:
There is a number sequence that is 2, 6, 12, 20, 30, …, and so on. Then what is the pattern of the 12th number? To answer this question, use the formula listed in the previous discussion
Un = n(n+1)
U12 = 10(12+1)
U12 =10(13)
U12 =130
So that the result of the rectangular number pattern in the example problem above is 130. Using a formula that is simple and easy to understand.
7. Square Numbers Pattern
Of the various number patterns, this square number pattern is one of them. Similar to the rectangular pattern, but still has differences.
A square number pattern is an arrangement of numbers whose pattern resembles a square. This number pattern is also formed by square numbers.
The arrangement of square numbers is 1, 4, 9, 16, 25, and so on. While the formula used to calculate the pattern of square numbers is Un = n2 (square).
Problems example:
Same with the various number patterns before. To help you better understand the pattern of square numbers, there are examples of questions as practice. So it’s easier to learn.
To understand more quickly, consider examples of questions about square number patterns such as: From a number sequence, namely 1, 4, 9, 16, 25, 36, … to 1.
What is the 12th number pattern in the square number pattern? To answer, use the formula listed above so that the calculation becomes:
Un = N2
U12 = 122
U12 = 144
From these calculations, it can be concluded that the result of the 12th square number pattern is 144.
8. Fibonacci Number Patterns
Is one of the many kinds of pattern numbers. The Fibonacci number pattern is a number arrangement that starts with the numbers 0 and 1.
The next one is obtained by adding the two previous numbers. Meanwhile, the formula itself is Un = (n-1) + (n-2).
As additional information, the number 2 in the Fibonacci numbers is obtained from the addition of 1 + 1.
While the number 3 is the result of the addition of 2 + 1, the number 5 is the result of the addition of 3 + 2, and so on.
Problems example:
To make it easier, just go to the example questions. Know the sequence of numbers 2, 2, 4, 6, 10, 16, …. Find the 7th and 8th terms in the sequence.
Then by using the concepts and Fibonacci formulas, the calculation is obtained:
N7 = 10+16 = 26
N8 = 10+16 = 26
That was an explanation of the various number patterns. Maybe some of you need it as teaching material or reference, everyone can help.
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