What is an Arithmetic Sequence: Definition, Formula, and Calculation Examples

YOGYAKARTA - What is an arithmetic sequence? In mathematics lessons, arithmetic sequences are one of the basic concepts that have many benefits in daily life.

With an arithmetic sequence, one can calculate savings regularly, calculate distance and speed, calculate single interest, even, predict the number of population growth.

So, what is meant by an arithmetic sequence? Check out the complete information in the article below.

What is an Arithmetic Sequence?

Quoted from the Fmipa Unesa website, it is a sequence of numbers where each subsequent term is obtained by adding a fixed number to the previous term. The fixed value is known as the difference (b).

For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence because the difference between each successive term is 3. The same is true for the sequence 20, 15, 10, 5 which has a difference of -5.

Furthermore, the numbers that form a sequence are called terms and are usually denoted by Un. For example, the number 1 is the first term (U1), the number 3 is the second term (U2), the number 5 as the third term (U3), and so on. The first term in the sequence is mathematically symbolized by the letter a.

Properties of Arithmetic Sequences

To recognize an arithmetic sequence, there are several main characteristicsthat need to be considered. Among others:

It has a fixed or constant difference (difference) between two consecutive terms. It can be ascending if the difference is positive.

By understanding the above characteristics, students can more quickly recognize and determine whether a sequence of numbers is an arithmetic sequence or not.

The formula for the arithmetic sequence

In an arithmetic sequence, there is a general formula to determine thevalue of the nth term. The formula is:

Un = a + (n - 1)b

Un = nth term, n = first term, b = number of terms, d = difference of terms

This formula is very helpful when we want to find the value of a term without having to write the entire series.

Examples of Arithmetic Sequences

For example, it is known that an arithmetic sequence with the first term4 and the difference 6. Find the 10th term of the sequence.

Using the formula, we obtain Un = 4 + (10 - 1) × 6 = 4 + 54 = 58. So, the 10th term is 58.

The Benefits of Arithmetic Series

Here are some of the benefits of arithmetic sequences that you need to know:

Improve the ability to think logically and systematically: Arithmetic sequences help students understand the relationship between numbers in sequence, thus training a logical and structured mindset. Make it easier to solve math problems: The concept of arithmetic sequences is often used in exam questions and is the basis for understanding advanced material such as arithmetic series. Useful in financial calculations: The benefits of arithmetic sequences can be felt in calculating periodic salary increases, regular savings, fixed installments, and budget planning. Save time in calculations: With the nth term formula, calculations can be done without having to write down all the members of the sequence. Become the basis for learning advanced mathematics: Arithmetic sequences play an important role as a foundation for studying patterns of numbers, functions, and higher level mathematics. Can be applied in daily life: For example, to calculate the increase in the number of items, the distance traveled gradually, or the increase in value that is fixed.

That's the explanation of what is an arithmetic series. Come on, visit VOI.id to get updates on other selected news.

Tag: matematika pengetahuan sains