Find the term of the sequence calculator

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

1. 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}

2. 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}

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Similarly, you can try the online sequence calculator to find the sequence for the following: 

• Arithmetic sequence, first term(a) = 5, common difference(d) = 10
• Geometric sequence, first term(a) = 4, common ratio(r) = 5

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• Geometric sequence

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