Arithmetic Sequence Calculator

Enter the first term of your sequence. This is the starting number.

Enter the common difference. This is the constant amount added to each term.

Enter the number of terms you want to calculate. This tells the tool how many values to generate.

Click Calculate. Your results appear instantly with the nth term, sum of all terms, and the complete sequence list.

An arithmetic sequence is a list of numbers where each term increases by the same fixed amount. This fixed amount is the common difference. If the common difference is positive, the sequence grows. If negative, the sequence decreases.

Example: 3, 7, 11, 15, 19

In this sequence, the first term is 3. The common difference is 4. Each number is 4 more than the previous number.

An arithmetic sequence follows a clear pattern. The pattern makes it easy to predict future terms without listing every value.

The formula for the nth term of an arithmetic sequence is:

Where:

• aₙ is the nth term you want to find
• a₁ is the first term of the sequence
• n is the position of the term in the sequence
• d is the common difference

This formula lets you jump directly to any term in the sequence. You do not need to calculate all the terms before it.

The explicit formula for an arithmetic sequence is the same as the nth term formula. It is called explicit because it gives you the value of any term directly based on its position.

This differs from a recursive formula. A recursive formula defines each term based on the previous term. The explicit formula is faster for finding distant terms.

The formula for the sum of the first n terms is:

Alternative form using the nth term:

Where:

• Sₙ is the sum of the first n terms
• n is the number of terms to add
• a₁ is the first term
• d is the common difference
• aₙ is the nth term

The sum formula saves time. Instead of adding each term individually, you get the total in one calculation.

Solving arithmetic sequence problems requires identifying the given values and selecting the right formula.

Arithmetic refers to the branch of mathematics dealing with numbers and basic operations. These operations include addition, subtraction, multiplication, and division.

In the context of sequences, arithmetic describes a pattern where you add or subtract the same value repeatedly. The word comes from the Greek arithmos, meaning number.

An arithmetic sequence uses addition as its core operation. Each term is the previous term plus the common difference.

This differs from a geometric sequence, where you multiply by a constant ratio instead of adding a constant difference.

Arithmetic sequences add a constant difference.

Geometric sequences multiply by a constant ratio.

Arithmetic sequences grow linearly. The increase is steady and predictable.

Geometric sequences grow exponentially. The increase accelerates with each term.

Use arithmetic sequences for linear growth patterns like savings with fixed deposits.

Use geometric sequences for exponential growth patterns like compound interest.

Instant Results: You get your answers in seconds. No manual calculations needed.

Multiple Outputs: The tool provides the nth term, sum, and full sequence list in one calculation.

Error-Free Accuracy: The calculator eliminates human calculation errors. Your results are always mathematically correct.

Step-by-Step Learning: The formulas and examples on this page help you understand the process. You learn while you calculate.

Free and Accessible: No registration required. No cost. Use it as many times as you need.

Start calculating now. Enter your first term, common difference, and number of terms above. Get instant, accurate results for your arithmetic sequence problems.