Arithmetic Sequence Calculator

Enter any 3 parameters to calculate the other 2 values

Enter number of terms (n):

Enter first number (a):

Enter common difference (d):

The nth term (an) is:

Sum of first n terms:

Result

Calculation Steps

Arithmetic Sequence Calculator Introduction

An arithmetic sequence is a sequence of numbers in which the difference between any two adjacent terms (i.e., the common difference) is constant. The Arithmetic Sequence Calculator is an intelligent mathematical tool that can automatically calculate the two unknown parameters of an arithmetic sequence based on any three known parameters entered by the user. The calculator supports all possible parameter combinations and displays detailed calculation steps to help users understand the computation process. Supported combinations are as follows:

Known a, d, n → Calculate a_n, S_n
Known a, a_n, n → Calculate d, S_n
Known a, d, S_n → Calculate n, a_n
Known a, a_n, S_n → Calculate n, d
Known d, n, S_n → Calculate a, a_n

Arithmetic Sequence Calculator Usage Instructions

Enter any three parameters (e.g., number of terms n, first term a, common difference d, etc.)
Click the "Calculate" button (or press the Enter key)
View results: The remaining two parameters are automatically filled in, along with detailed calculation steps
Example usage: Click the "Example" button to obtain a random example (two parameters are automatically left blank)
Click the "Clear" button to reset all inputs

Basic Formulas

1. Common Difference (d): d = a_n - a_n-1

2. n-th Term Formula: a_n = a₁ + (n-1) × d

3. Sum of First n Terms Formula: S_n = n/2 × (a₁ + a_n)

Or S_n = n/2 × [2a₁ + (n-1)d]