# Write a rule for the nth term of the sequence

You can dive straight into using it or read on to discover how it works. In this article, we explain the arithmetic sequence definition, clarify the sequence equation that the calculator uses, and hand you the formula for finding arithmetic series sum of an arithmetic progression. Sequences are useful in a number of mathematical disciplines for studying functionsspacesand other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for serieswhich are important in differential equations and analysis.

Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers. There are a number of ways to denote a sequence, some of which are more useful for specific types of sequences. One way to specify a sequence is to list the elements. For example, the first four odd numbers form the sequence 1, 3, 5, 7. This notation can be used for infinite sequences as well.

## What is an arithmetic sequence?

For instance, the infinite sequence of positive odd integers can be written 1, 3, 5, 7, Listing is most useful for infinite sequences with a pattern that can be easily discerned from the first few elements. Other ways to denote a sequence are discussed after the examples.

Examples[ edit ] A tiling with squares whose sides are successive Fibonacci numbers in length. The prime numbers are the natural numbers bigger than 1 that have no divisors but 1 and themselves. Taking these in their natural order gives the sequence 2, 3, 5, 7, 11, 13, 17, The prime numbers are widely used in mathematics and specifically in number theory.

The Fibonacci numbers are the integer sequence whose elements are the sum of the previous two elements. The first two elements are either 0 and 1 or 1 and 1 so that the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, Other examples of sequences include ones made up of rational numbersreal numbersand complex numbers.

In fact, every real number can be written as the limit of a sequence of rational numbers, e. This sequence does not have any pattern that is easily discernible by eye, unlike the preceding sequence, which is increasing. One such notation is to write down a general formula for computing the nth term as a function of n, enclose it in parentheses, and include a subscript indicating the range of values that n can take.

For example, in this notation the sequence of even numbers could be written as.In this example, to get from the position to the term, take the position number and add 4. If the position is, then the position to term rule is.. The nth term.

The th term of a sequence is the. th Term Rule Nth term rule – the equation that allows you to find any term in the sequence T n – the term in the “nth” position n – the position of the term of a sequence a Write an nth term rule for the following sequences. a. 11, 13, 15, 17, b. 5, , ,, . The following geometric sequence calculator will help you determine the nth term and the sum of the first n terms of an geometric sequence. Guidelines to use the calculator If you select a n, n is the nth term of the sequence.

Write the equation for the nth term in a sequence using your newly found coefficients. Example: nth term in the sequence = n^3 + 2n^2 + 3n + 5 Plug in your desired value of n into the equation and calculate the nth term in the sequence. Write a rule for the nth term of the arithmetic sequence - 1.