Sequence Inputs

Sequence Results

N-th Term Value
0
Sum of N Terms
0
Sequence Formula
aₙ = 0
First Few Terms
-

An Arithmetic Sequence Calculator is a practical mathematical tool designed to find any specific number within a linear sequence. It also quickly calculates the total sum of all the numbers in that sequence. This tool is widely used in algebra, financial forecasting, and pattern analysis.

Understanding Arithmetic Sequences

An arithmetic sequence is a list of numbers where the step between each consecutive number remains exactly the same. This constant step is known as the "Common Difference".

The standard formula to find any specific term in the sequence is:

aₙ = a₁ + (n - 1) × d

In this formula, a₁ is the very first number, d is your constant step or difference, and n is the position of the number you are trying to find.

How to Use This Calculator

  • Enter the First Term of your sequence. This is where your number pattern begins.
  • Enter the Common Difference. If your sequence goes up by 4 each time, enter 4. If it goes down by 2, enter -2.
  • Enter the Number of Terms. For example, if you want to know the 15th number in the sequence, enter 15 here.
  • The calculator will instantly display the value of that specific term, the sum of all terms up to that point, and a preview of how your sequence begins.

Frequently Asked Questions

What is the difference between an arithmetic and a geometric sequence?

In an arithmetic sequence, you always ADD or SUBTRACT the same amount to get to the next number (like 2, 4, 6, 8). In a geometric sequence, you always MULTIPLY or DIVIDE by the same amount to get to the next number (like 2, 4, 8, 16).

How is the sum of the sequence calculated?

The sum of an arithmetic sequence (also called an arithmetic series) is found by averaging the first and last term, and then multiplying by the total number of terms. The formula looks like this: Sₙ = (n ÷ 2) × (a₁ + aₙ).

Can the common difference be a negative number?

Yes. If the common difference is a negative number, your sequence will decrease over time. For example, starting at 10 with a difference of -3 will create the sequence 10, 7, 4, 1, and so on.