Arithmetic Sequence Sum Calculator

Enter First Term, Common Difference, Number of Terms → Get General Term and Sum in One Click

Input Parameters

Calculation Results

General Term Formula:—
Sum Formula:—
nth Term:—
Sum of Sequence:—

Introduction
General Term
Sum Formula
Common Scenarios
Mnemonics/Examples

Introduction

An arithmetic sequence (or arithmetic progression) is a sequence where the difference between consecutive terms is constant. It is widely used in mathematics, physics, finance, programming, and other fields.

General Term Formula

aₙ = a₁ + (n-1)d

a₁: First term
d: Common difference
n: Number of terms

Sum Formula

Sₙ = n(a₁ + aₙ)/2
or
Sₙ = n[2a₁ + (n-1)d]/2

Common Scenarios

Students: Sequence exercises, competitions
Teachers: Classroom demonstrations, assignment generation
Finance: Equal installment payments, tiered billing
Programming: Accumulative summation, loop efficiency

Mnemonics & Examples

Mnemonic: Add the first term to the last term, multiply by the number of terms, then divide by two.
Example: a₁=3, d=2, n=10 → 10th term = 21, sum = 120

First Term	Common Difference	Number of Terms	nth Term	Sum
3	2	10	21	120