# Number sequence calculator for instant results

Discover the features of our free sequence calculator.

Calculate the terms of a number sequence in a blink of an eye.

## Arithmetic Sequence Calculator

definition: an = a_{1} + f × (n-1)

example: 1, 3, 5, 7, 9 11, 13, ...

## Geometric Sequence Calculator

definition: an = a × r_{n-1}

example: 1, 2, 4, 8, 16, 32, 64, 128, ...

## Fibonacci Sequence Calculator

definition: a_{0}=0; a_{1}=1; a_{n} = a_{n-1} + a_{n-2};

example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

### What is the definition of the sequences calculator?

A number sequence calculator is an easy-to-use tool that helps you find out the terms of sequences in a breeze. You can use our calculator to determine both finite and infinite sequences in just a few seconds. Our tool is equally helpful for arithmetic sequences, geometric sequences, and Fibonacci sequences.

### Arithmetic sequence

An arithmetic sequence in math is a sequence of numbers where the difference between each consecutive term is constant. The next term is created by adding a constant number to the previous term. This number is also called a constant difference.

Depending on its sign, an arithmetic sequence can be either positive or negative, consecutively tending toward positive or negative infinity.

To denote this sequence, we can use an arithmetic sequence formula:

a

_{n}= a_{1}+ f × (n-1), where an is the n^{th}term in the sequence, a_{1}is the is the first term, and f is the common difference.or a

_{n}= a_{m}+ f × (n-m)i.e. a

_{1}, a_{1}+ f, a_{1}+ 2f.For example, 1, 3, 5, 7, 9, 11, 13, ...

Here, the common difference, or f, is 2. Let's use the equation to determine the fifth term:

a

_{5}= a_{1}+ f × (n-1)a

_{5}= 1 + 2 × (5-1)a

_{5}= 1 + 8 = 9### Geometric sequence

A number sequence, in which each next term after the first one is created by multiplying the previous term by a set non-zero number, is called a geometric sequence. This fixed number is also referred to as a common ratio.

The geometric sequence formula is as follows:

a

_{n}= a × r^{n-1}, where an is the n_{th}term, a refers to the scale factor, and r – common ratio.i.e. a, ar, ar

^{2}, ar^{3}, ...For instance, 1, 2, 4, 8, 16, 32, 64, 128, ... It is clear that in this example, the common ratio, or r, is 2.

Say, we wanted to calculate the eighth term in the sequence using the formula above:

a

_{8}= a × r^{8-1}a

_{8}= 1 × 2^{7}= 128You can also find out the sum of the geometric equation with this formula:

### Fibonacci sequence

In a Fibonacci sequence, each next term following the first two is a sum of two previous terms. Based on the chosen starting point, the first two terms can be either 1 and 1 or 0 and 1.

Fibonacci numbers appear commonly yet unexpectedly and have numerous applications in mathematics and beyond. They are often used in computer studies, biological settings, and even economics.

The Fibonacci sequence formula is:

a

_{n}= a_{n-1}+ a_{n-2}, where an is the n^{th}number in the sequence.An example of a Fibonacci sequence is: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

a

_{0}= 0; a_{1}= 1;## Frequently Asked Questions

Our calculator allows you to determine the numbers of your sequence in an instant. Furthermore, you can use it for any sequence of numbers, be it arithmetic, geometric, or Fibonacci list. We also do calculations for common sequences, such as prime numbers.

Calculating a sequence is as easy as pie with our free tool! Just follow these three simple steps.

Step one: Insert the first number (a) and the common difference (d) or common ratio (r) in the respective field.

Step two: Hit the "Calculate" button.

Step three: Clear the fields by tapping on the "Reset" button.

A sequence calculator captures and mathematically represents the common relationship (difference, ratio, etc.) behind two consecutive terms in the sequence.

To grasp the whole meaning of this calculating tool, you need to understand what a sequence of numbers is. A sequence is the ordered list of numbers or terms governed by a specific pattern. The order and increasing and decreasing numbers are vital for a sequence.

The common depiction of a sequence is:

a

_{1}, a_{2}, a_{3}, … a_{n}There are two types of sequences in math:

- A finite sequence, which obtains a definite amount of numbers;
- An infinite sequence, which is an endless set of terms.

A common pattern is the most important thing for any sequence. These factors can be found in the simplest things, like the clock rotation as well as in complicated equations.

Finding such a pattern requires time and attention to detail. For an unknown sequence, you have to discover a difference between two elements of the list and do the same for all the elements.

But worry not! Our calculator can make this tedious task as easy as a walk in the park. Use it at any time for effortless calculations and save hours of time and tons of energy.

Arithmetic sequences are very common in our day-to-day lives. Stacking household items, arranging seats in a classroom, and finding a leap earl all require an arithmetic sequence.

The arithmetic sequence formula is also frequently used to calculate the terms of said sequence.

For example, we need to find the thirteenth term in the sequence 1, 5, 9, 13... Given that the common difference d is 4, and the first term a1 is 1, we can use the following equation:

a

_{n}= a_{1}+ (n - 1) da

_{13}= 1 + (13 - 1)4a

_{13}= 1 + (12)4a

_{13}= 1 + 48a

_{13}= 49Whatever you need an arithmetic sequence for, our efficient tool can help you with calculations.

We guarantee the most accurate results and seamless experience every step of the way.