How to find the first four terms of the sequence

In mathematics, a sequence is an ordered list of objects. Accordingly, a number sequence is an ordered list of numbers that follow a particular pattern. The individual elements in a sequence is often referred to as term, and the number of terms in a sequence is called its length, which can be infinite. In a number sequence, the order of the sequence is important, and depending on the sequence, it is possible for the same terms to appear multiple times.

An ordered list of numbers is called a sequence. Each number of the sequence is called a term. The three dots represent that the sequence goes on to infinity. A sequence is called an arithmetic sequence if the difference between the two terms is constant. While observing the above example it can be easily identified that 3 is added to the first term of the sequence to get the second term and similarly adding 3 to the second term to get the third term and so on. Therefore, the rule for defining an arithmetic sequence will be as. In this example, we can observe that there is a difference between the two consecutive terms, that is -5, which is the common difference.

How to find the first four terms of the sequence

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Use this number sequence calculator to easily calculate the n-th term of an arithmetic, geometric or fibonacci sequence, and the sum of all terms between the starting number and the nth term. In mathematics, a sequence is an ordered list of objects , usually numbers, in which repetition is allowed. The number of elements is the length of the sequence. Number sequences can be expressed as the function that generates the next term in a sequence from the previous one. Sequences can be monotonically increasing - that is if each term is greater than or equal to its preceding term, or they can be monotonically decreasing , if the reverse is true. If each element is larger than or smaller than the preceding element, then a sequence is strictly monotonically increasing or strictly monotonically decreasing, respectively. Our sequence calculator outputs subsequences of the specified sequence around the selected nth element. This is a very versatile calculator that will output sequences and allow you to calculate the sum of a number sequence between a starting item and an n-th term, as well as tell you the value of the n-th term of interest.

How to find the first four terms of the sequence

A video game company launches an exciting new advertising campaign. They predict the number of online visits to their website, or hits, will double each day. The model they are using shows 2 hits the first day, 4 hits the second day, 8 hits the third day, and so on. See Table 1. If their model continues, how many hits will there be at the end of the month? In this section, we will explore these kinds of ordered lists. One way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers.

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This difference can either be positive or negative, and dependent on the sign will result in terms of the arithmetic sequence tending towards positive or negative infinity. This article is being improved by another user right now. Enhance the article with your expertise. You can suggest the changes for now and it will be under the article's discussion tab. Hire With Us. Please Login to comment Contribute your expertise and make a difference in the GeeksforGeeks portal. In a number sequence, the order of the sequence is important, and depending on the sequence, it is possible for the same terms to appear multiple times. The formula for the n th term as mentioned above is,. Add Other Experiences.

The yearly salary values described form a geometric sequence because they change by a constant factor each year. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio.

While observing the above example it can be easily identified that 3 is added to the first term of the sequence to get the second term and similarly adding 3 to the second term to get the third term and so on. The equation for calculating the sum of a geometric sequence:. Report issue Report. Arithmetic Sequence A sequence is called an arithmetic sequence if the difference between the two terms is constant. Please Login to comment An ordered list of numbers is called a sequence. What is the common difference of four terms in an AP? Enhance the article with your expertise. A Fibonacci sequence is a sequence in which every number following the first two is the sum of the two preceding numbers. Accordingly, a number sequence is an ordered list of numbers that follow a particular pattern. The general form of a geometric sequence can be written as:. What are some Real Life Applications of Trigonometry?