logo
logo
Sign in

Number Sequence Calculator | Sequence definition and computation

avatar
AllCalculator
Number Sequence Calculator | Sequence definition and computation

How can you define an arithmetic sequence?


It is important first to understand what sequence means to be able to answer this question. Sequences are collections of objects that appear in a specific order, such as numbers or letters. The elements in a sequence are called terms or elements of the sequence. The same object appears quite often in a sequence more than once. Mathematical sequences are also objects. They are numbers. You add a constant number (called the common difference) to create each consecutive number. Sequences like that can be finite if there are a set number of terms (for example, 20) or infinite if you don't. The common difference and the first term are the only two coefficients that can uniquely define each arithmetic sequence. Knowing these two values enables you to write down the entire sequence in a step-by-step fashion.


Different naming conventionsAllcalculator.net's are used for arithmetic sequences, so you may need some clarification if you start exploring the topic of an arithmetic sequence. Arithmetic sequence and series are two terms that may be encountered. These are also called arithmetic progression and partial sum, respectively. It is important to distinguish between series and sequence because, by definition, arithmetic series is composed of the sum of n terms. In contrast, the arithmetic sequence is simply the addition of common differences.


How do arithmetic and geometric sequences differ?


Any arithmetic sequence has a constant difference between adjacent terms, but all geometric sequences have a constant ratio between consecutive terms. A common difference between the previous and the next term determines the arithmetic sequence term. Taking the previous geometric sequence term and multiplying it by a common ratio gives you the next geometric sequence term.


What is the use of an arithmetic sequence calculator?


When given the nth value of the sequence and the common difference between the terms, we learned how to generate the arithmetic sequence. Now let's look at how to use the arithmetic sequence generator to do the same calculations. We will continue with the example that was discussed above. We are given the information that the 5th term in a sequence is 20. We are also given the information that there is a difference of 2 between the terms. This can be achieved by following the steps below:


  • Having been given the 5th term of the sequence, we will enter 5 in the box given for n. Originally, 5 was the value for n, but now it will be 5 for n
  • Next, we will enter the nth value of the arithmetic sequence calculator corresponding to the term n we previously entered in the first step. Because 20 is the 5th term of a sequence, we will enter it as the nth value
  • Using the arithmetic sequence calculator, we will enter two against the common difference box to specify the common difference between the terms
  • This calculator calculates arithmetic sequences up to ten terms at a time. In the box "Total number of terms", we will enter 1
  • We have now filled in all the necessary information, and we need to find the arithmetic sequence by clicking the calculate button.


collect
0
avatar
AllCalculator
guide
Zupyak is the world’s largest content marketing community, with over 400 000 members and 3 million articles. Explore and get your content discovered.
Read more