What Is Aritmetic Series?

Desember 29, 2022 Posting Komentar

Soal Barisan Dan Deret — What Is Aritmetic Series?

What is Aritmetic Series?

Aritmetic Series is a series of numbers in which each term is obtained by adding a fixed number to the preceding term. It is a type of sequence or progression in which each number is the sum of the two numbers before it. It is also known as an arithmetic progression (AP). In a arithmetic series, the common difference between any two consecutive terms is a constant.

What are the Types of Aritmetic Series?

There are two types of Aritmetic Series, namely finite and infinite. A finite Aritmetic Series has a limited number of terms, while an infinite Aritmetic Series has an unlimited number of terms.

Example of Finite Aritmetic Series

A finite Aritmetic Series can be expressed in the form a, a + d, a + 2d, a + 3d,...,a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms in the series. For example, the following is a finite Aritmetic Series with a = 10, d = 5, and n = 4: 10, 15, 20, 25.

Example of Infinite Aritmetic Series

An infinite Aritmetic Series can be expressed in the form a, a + d, a + 2d, a + 3d,..., where a is the first term and d is the common difference. For example, the following is an infinite Aritmetic Series with a = 10 and d = 5: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,...

How to Solve Aritmetic Series?

There are various methods to solve Aritmetic Series. One of the most common methods is to use the formula S = n/2(2a + (n-1)d), where S is the sum of the terms in the series, n is the number of terms, a is the first term, and d is the common difference. For example, the sum of the terms in the following Aritmetic Series can be calculated using this formula: 10, 15, 20, 25, 30.

In this example, the first term is 10, the common difference is 5, and the number of terms is 5. Applying the formula, we have S = 5/2(2*10 + (5-1)*5) = 5/2(20 + 20) = 100. Therefore, the sum of the terms in the series is 100.

Contoh Soal Deret Aritmatika

Berikut ini adalah beberapa contoh soal deret aritmatika:

Soal 1

Diketahui deret aritmatika: 2, 7, 12, …, 42. Tentukan jumlah anggotanya!

Jawaban 1

Jumlah anggota deret aritmatika adalah 6, yaitu 2, 7, 12, 17, 22, dan 42.

Soal 2

Diketahui deret aritmatika: 7, 10, 13, …, 28. Tentukan jumlah anggotanya!

Jawaban 2

Jumlah anggota deret aritmatika adalah 5, yaitu 7, 10, 13, 16, dan 28.

Conclusion

Deret aritmatika adalah salah satu jenis deret yang didefinisikan dengan menambahkan jumlah tetap pada setiap anggota berikutnya. Secara umum, dapat dinyatakan dalam bentuk a, a + d, a + 2d, a + 3d,...,a + (n-1)d, dengan a adalah anggota pertama, d adalah beda umum, dan n adalah jumlah anggota dalam deret. Dengan menggunakan rumus S = n/2(2a + (n-1)d), jumlah anggota dalam deret aritmatika dapat ditentukan.