Arithmetic Sequence Calculator
Using an Arithmetic Sequence Calculator can help you in finding an arithmetic sequence within seconds. This handy tool has helped students in solving their problems related to sequence creation. For students, it is not an easy task to create an arithmetic sequence as they have to perform different operations including addition, subtraction, and multiplication at the same time.
This maths calculator has been designed for users of all ages and all levels. Doesn’t matter what is your level of understanding, you can use this Arithmetic Sequence Calculator. It will allow you to get an arithmetic sequence from any two values and the common difference between two consecutive terms.
Table of Contents
Arithmetic Sequence Definition
In Mathematics, Arithmetic sequence means a particular type of sequence in which two consecutive terms can be found by adding or subtracting the same constant number called the common difference.
To find the next terms of this sequence, we need to add a constant number in the previous value. Similarly, we can find the previous term of the sequence by subtracting the same number from the next value of the sequence.
For example, 2, 8, 14, and 20 are in Arithmetic sequence as there is a difference of the same number i.e. “6”. Similarly, we can write an arithmetic sequence using a single value and the common difference between the values.
Arithmetic Sequence Formula
In general, the formula for Arithmetic Sequence is:
an = a1 + (n-1)d
In the above formula,
- a n stands for the nth term of the sequence.
- a1 is the first term of the sequence.
- n is the total number of terms.
- d is the common difference between the terms of the sequence.
How to Calculate the Arithmetic Sequence?
To calculate the Arithmetic sequence, we only need to put the values in the above formula. If we know any two consecutive terms of the sequence or the first term with a common difference, we can find a sequence from them. Let us explain with an example to let you understand the process to calculate arithmetic sequences properly.
Example 1:
Find the nth term of the Arithmetic sequence with 12 numbers in total if the first term is 4 and the common difference is 7.
Solution:
As we know,
an = a1 + (n-1)d
From the question, we know,
a1= 4
n = 12
d = 7
So, we can find the nth term by putting values in the above formula.
a12 = 4 + (12 - 1)7
= 4 + (11)7
= 4 + 77
a12 = 81
Example 2:
Find the 3rd term of the sequence if the first term is 11 while the common difference is 21.
Solution:
From the question, we know,
a1= 11
From the question, we know,
n = 3
d = 21
Also,
a3 = ?
By putting values in the formula,
a3 = 11 + (3 - 1)21
= 11 + 42
= 53
How to use the Arithmetic Sequence Calculator?
To make the process of Arithmetic Sequence creation easy, you can use Arithmetic Sequence Calculator offered by Claculator’s Bag. This tool has a simple interface that can be followed by anyone.
- Insert the common difference in the top-most box
- Enter the first value of the sequence
- This calculator will automatically show the next 4 terms of the sequence
FAQ | Arithmetic Sequence
How do you find the pattern rule of a sequence?
Every type of sequence has a particular pattern rule that can be found by analyzing the terms. For example, the pattern rule of an Arithmetic sequence can be found by addition or subtraction.
What is the main principle of an arithmetic sequence?
The main principle of an arithmetic sequence is the difference between two consecutive terms will remain constant throughout the sequence.
How do you find the arithmetic Sequence?
To find an arithmetic sequence, we only need to add the common difference in the first term to get the second term. Similarly, we can find the third term by adding the same constant number in the second term. In this way, we can find as many terms of the sequence as we need in it.
How do I find the common difference in an arithmetic sequence?
To find the common difference, we need to subtract the previous term from the upcoming one. In simple words, you need to subtract the first term from the second one.
How do I find the nth term of an arithmetic sequence?
To find the nth term of the arithmetic sequence, you need to follow this specific formula.
an = a1 + (n-1)d
