# Sequence Formula Calculator Or Sequence Calculator

**Created By :** Abhinandan Kumar

**Reviewed By :** Phani Ponnapalli

**Last Updated :** Mar 24, 2023

Finding the correct Sequence Formula isn't difficult anymore with this handy tool Sequence Formula Calculator. Simply provide the inputs and enter for values that you don't know and find out the formula for the sequence provided in no time.

### What is Meant by the Sequence?

The sequence is a collection of objects in which repetitions are allowed and order is important. What are the Different Types of Sequences?

**Arithmetic sequence**: A sequence in which every successive term differs from the previous one is constant, is called Arithmetic Sequence.

E.g. Suppose in a sequence a1, a2, a3, …., an are the terms & difference between each term is ‘d’, then the formula is given by an = a1 + (n−1)d

**Geometric Sequence:** A sequence in which every successive term has a constant ratio is called Geometric Sequence.

E.g. Suppose in a sequencea1, a2, a3, …., anare the terms & ratio between each term is ‘r’, then the formula is given byan=(an – 1) × r

**Harmonic Sequence:** It is a series formed by taking the inverse of arithmetic series.

E.g. Harmonic series looks like this 1/a1, 1/a2, 1/a3, ……. Where a2 = a1 + d ; a3 = a2 + d & so on…

**Fibonacci Sequence:** A sequence in which two consecutive terms are added to get the next consecutive 3rd term is called Fibonacci Sequence.

E.g. Suppose in a sequence a1, a2, a3, …., anare the terms & a3 = a2 + a1 & so on…. Formula is given by an = an-2 + an-1, n > 2

**Sequence of Prime Numbers:** A prime number is a number that is not divisible by any other number except one & that number, this sequence is infinite, never-ending.

E.g. This is a sequence of prime numbers – 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, ….. & so on

**Second Degree Polynomial:** It is a polynomial where the highest degree of a polynomial is 2. It is also called a quadratic polynomial.

E.g. It is represented in the form as f(x)=Ax^2+Bx+C, where A, B, C are constants. Understand the concept in more detail with the explanations and procedure listed for Sequences. Visit sequencecalculators.com, the best place for learning, and get various calculators for making your job easier.

### How to Find the Formula of a given Sequence?

The steps for finding the formula of a given arithmetic sequences are given below:

**Step 1:** Find the difference consecutive terms in the sequence & check whether the difference is the same for each pair of terms. For example, consider a sequence 3,17,? ,45....

**Step 2:** Heck for missing numbers by checking the difference. It should be the same in every case. Wherever it is not, we can add the common difference to the number before the space of the missing number in the sequence.

In the above example taking A1=3 and An=45. Assuming the sequence as Arithmetic Sequence and solving for d, the common difference, we get,

45 = 3 + (4-1)d

42= 3d

14 = d

Hence, by adding 14 to the successive term, we can find the missing term.

**Step 3:** Repeat the above step to find more missing numbers in the sequence if there.

**Step 4:** We can check our answer by adding the difference, “d” to each term in the sequence to check whether the next term in the sequence is correct or not.

**Step 5:** After finding the common difference for the above-taken example, the sequence becomes 3, 17, 31, 45..... and the missing term is 31. Hence, we can state that the given sequence is Arithmetic Sequence.

**Step 6:** After finding the type of Sequence. We can easily determine the formula

### FAQs On Sequence Formula Calculator with Steps

**1. How do you write a sequence?** While writing a sequence you need to list all its elements. For instance, the sequence of the first four even numbers is given 0,2,4,6. The same notation can used for infinite sequences also. For example, the infinite sequence of positive even integers is (0,2,4,6, ....).

**2. What is a sequence equation for Arithmetic Sequences?** An arithmetic sequence can be determined by an explicit formula in which an = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a1.

**3. How do you determine the formula for the given sequence?** To find the sequence formula for the given numbers, you can use the online sequence formula calculator or else check out the manual process from our page.