Sequence & Series Calculator

All math tools

Calculate terms and sums for Arithmetic and Geometric progressions.

Progression Parameters

First Term (a₁)

Common Difference (d)

Number of Terms (n)

Sequence Analysis

100

Sum of n Terms (Sₙ)

Calculated based on the sequence's growth pattern.

nth Term (aₙ)19

About this calculator

Quick Reference

Growth TypeLinear

Infinite SumDivergent

What are Sequences and Series?

A sequence is an ordered list of numbers. A series is the sum of the terms of a sequence. The two most common types are Arithmetic (constant difference) and Geometric (constant ratio).

💡

Pro Tips

Arithmetic sequences grow linearly (constant speed).
Geometric sequences grow exponentially (accelerating speed).
If |r| < 1, an infinite geometric series has a finite sum: a₁/(1-r).

Fun Facts

"The fibonacci sequence is neither arithmetic nor geometric but appears everywhere in nature."
"The 'sum of all natural numbers' until infinity is famously used in string theory (with specific regularization)."
"Arithmetic progressions were studied by ancient Egyptians as far back as 1550 BC."

Formula: Arithmetic: aₙ=a₁+(n-1)d, Geometric: aₙ=a₁rⁿ⁻¹