Find the first 6 terms of the sequence calculator

Sequence Calculator is a free online tool that displays the sequence of the given function. BYJU’S online sequence calculator tool makes the calculation faster, and it displays the sequence of the function in a fraction of seconds.

Table of Contents Show

How to Use the Sequence Calculator?
What is Meant by the Sequence?
About Arithmetic Sequence Calculator
What is a Sequence Calculator?
Sequence Calculator
How to Use Sequence Calculator?
How to Find Sequence Calculator?
Solved Examples on Sequence Calculator
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☛ Math Calculators:
What is the sequence calculator?
What are the 6 types of sequence?

How to Use the Sequence Calculator?

The procedure to use the sequence calculator is as follows:
Step 1: Enter the function and limit in the respective input field
Step 2: Now click the button “Calculate” to get the Sequence
Step 3: Finally, the sequence of the given function will be displayed in the new window

What is Meant by the Sequence?

In mathematics, the sequence is defined as the ordered list of numbers. Each number in the sequence is considered as a term. The three dots at the end of the sequence means that the pattern of numbers will be continued. There are four different types of sequence in Maths. They are:

Arithmetic sequence
Geometric Sequence
Harmonic Sequence
Fibonacci series

Also, read: Sequence and Series

An example of a sequence is 1, 3, 5, 7, 9,… Here, the first term is 1; the second term is 3; the third term is 5, and so on. Here, each term in the sequence has a difference of 2. Hence, the common difference of the sequence is 2, and the sequence will be continued by adding 2 to the previous term.

About Arithmetic Sequence Calculator

This Arithmetic Sequence Calculator is used to calculate the nth term and the sum of the first n terms of an arithmetic sequence.

FAQ

In mathematics, an arithmetic sequence, also known as an arithmetic progression, is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. The sum of the members of a finite arithmetic progression is called an arithmetic series.

If the initial term of an arithmetic sequence is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

an = a1 + (n - 1)d

The sum of the first n terms Sn of an arithmetic sequence is calculated by the following formula:

Sn = n(a1 + an)/2 = n[2a1 + (n - 1)d]/2

Sequences are lists of objects or numbers that are observed to have an order or follow a particular pattern or function. Sequences have been known to be both finite and infinite.

What is a Sequence Calculator?

'Sequence Calculator' is an online tool that helps to calculate arithmetic and geometric sequence. Online Sequence Calculator helps you to calculate the arithmetic and geometric sequence in a few seconds.

Sequence Calculator

How to Use Sequence Calculator?

Please follow the steps below to find the arithmetic sequence:

Step 1: Enter the first term(a), the common difference(d) or common ratio(r) in the given input box.
Step 2: Click on the "Calculate" button to find the sequence.
Step 3: Click on the "Reset" button to clear the fields and find the sequence for different values.

How to Find Sequence Calculator?

An arithmetic sequence is defined as a series of numbers, in which each term (number) is obtained by adding a fixed number to its preceding term. The general form of an arithmetic sequence can be written as:

an = a + (n - 1)d

Where 'an' is the nth term in the sequence, 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the nth term to be obtained.

A geometric sequence is a sequence where every term bears a constant ratio to its preceding term. The general form of a geometric sequence can be written as:

an = arn - 1

Where 'an' is the nth term in the sequence, 'a' is the first term, 'r' is the common ratio between two numbers, and 'n' is the nth term to be obtained.

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Solved Examples on Sequence Calculator

Example1:
Find the arithmetic sequence up to 5 terms if first term(a) = 6, and common difference(d) = 7 and verify it using the online sequence calculator.
Solution:
Given: a = 6, d = 7
an = a + (n - 1)d
a1(first term) = 6 + (1 - 1)7 = 6 + 0 = 6

a2(second term) = 6 + (2 - 1)7 = 6 + 7 = 13
a3(third term) = 6 + (3 - 1)7 = 6 + 14 = 20
a4(fourth term) = 6 + (4 - 1)7 = 6 + 21 = 27
a5(fifth term) = 6 + (5 - 1)7 = 6 + 28 = 34
Therefore, the arithmetic sequence is {6, 13, 20, 27, 34}
Example2:
Find the geometric sequence up to 5 terms if first term(a) = 6, and common ratio(r) = 2 and verify it using the online sequence calculator.
Solution:
Given: a = 6, d = 2
an = arn - 1

a1(first term) = 6 × 21 - 1= 6
a2(second term) = 6 × 22 - 1= 6 × 2 = 12
a3(third term) = 6 × 23 - 1= 6 × 4 = 24
a4(fourth term) = 6 × 24 - 1= 6 × 8 = 48
a5(fifth term) = 6 × 25 - 1= 6 × 16 = 96
Therefore, the geometric sequence is {6, 12, 24, 48, 96}