What is an arithmetic series?

An arithmetic series is the sum of terms in an arithmetic sequence, where each term is obtained by adding a fixed number (common difference) to the previous term. For example: 2 + 5 + 8 + 11 + 14 (difference = 3).

How do you find the sum of an arithmetic series?

Use the formula S = n/2 × (2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. Alternatively, S = n/2 × (first + last).

Can the common difference be negative?

Yes! A negative common difference creates a decreasing sequence. For example, with a = 10 and d = -2: 10, 8, 6, 4, 2. The calculator handles negative differences correctly.

What is the difference between arithmetic and geometric series?

In an arithmetic series, you add a constant to get the next term. In a geometric series, you multiply by a constant. Arithmetic: 2, 5, 8, 11 (+3). Geometric: 2, 6, 18, 54 (×3).

Arithmetic Series Sum Calculator

Calculate the sum of arithmetic sequences instantly. Find the sum of arithmetic series with step-by-step solutions. Perfect for students learning sequences and series.

First Term (a)

Common Difference (d)

Number of Terms (n)

Enter values to calculate arithmetic series sum

Arithmetic Series Sum Calculator Tool Introduction

A comprehensive Arithmetic Series Sum Calculator that computes the sum of arithmetic sequences with ease. Enter the first term, common difference, and number of terms to get instant results with detailed explanations.

Perfect for students studying sequences and series, teachers preparing lessons, and anyone working with linear patterns in mathematics, finance, or science. Understanding arithmetic series is fundamental to many areas of mathematics.

Our calculator shows you the formula used, step-by-step calculations, and can even display all terms in the sequence. It's an excellent learning tool for understanding how arithmetic progressions work.

All calculations are performed locally in your browser for complete privacy. No data is collected or stored. Use this tool to verify homework, understand arithmetic series, or solve real-world problems involving linear patterns.

Arithmetic Series Sum Calculator User Guide

How to Use

Enter First Term (a): The initial value of the sequence
Enter Common Difference (d): The constant added to each term
Enter Number of Terms (n): How many terms to sum
Click Calculate: Get the sum and detailed explanation

Understanding Arithmetic Series

An arithmetic series is the sum of terms in an arithmetic sequence, where each term is found by adding a constant (common difference) to the previous term.

Formula

Sum Formula: S_n = n/2 × (2a + (n-1)d)

Alternative: S_n = n/2 × (first term + last term)

Example

Sum of 2 + 5 + 8 + 11 + 14:

First term (a) = 2
Common difference (d) = 3
Number of terms (n) = 5
Last term = 2 + (5-1) × 3 = 14
Sum = 5/2 × (2 + 14) = 5/2 × 16 = 40

Key Features

Calculate arithmetic series sums
Step-by-step solution display
Show all terms in sequence
Support for negative differences
Calculate last term automatically
Mobile-friendly interface

Frequently Asked Questions

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