Geometric Sequence Calculator

This calculator helps you determine the terms of a geometric sequence given its first term, common ratio, and the number of terms. Whether you're a student, teacher, or math enthusiast, this tool simplifies the process of calculating geometric sequences.

Calculator

First Term (a₁) *

Common Ratio (r) *

Number of Terms (n) *

Results

Nth Term (a_n) N/A

Sum of First n Terms (S_n) N/A

Data Source and Methodology

This calculator uses the standard formulas for geometric sequences. All calculations are based on these formulas and data.

The Formula Explained

Nth Term Formula: a_n = a₁ * r^n-1

Sum Formula: S_n = a₁ * (1 - rⁿ) / (1 - r) if r ≠ 1

Glossary of Variables

a₁: First term of the sequence.
r: Common ratio.
n: Number of terms.
a_n: Nth term of the sequence.
S_n: Sum of the first n terms.

How It Works: A Step-by-Step Example

Suppose you have a sequence where the first term a₁ is 3, the common ratio r is 2, and you want to find the 5th term. Using the Nth term formula, you'd calculate a₅ = 3 * 2⁴ = 48.

Frequently Asked Questions (FAQ)

What is a geometric sequence?

A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

How do I find the common ratio?

The common ratio is found by dividing any term in the sequence by the previous term.

What happens if the common ratio is 1?

If the common ratio is 1, the sequence is not geometric as all terms are the same.

Can the common ratio be negative?

Yes, the common ratio can be negative, which results in the sequence alternating in sign.

How is the sum of the sequence calculated?

The sum of the first n terms of a geometric sequence is calculated using the formula S_n = a₁ * (1 - rⁿ) / (1 - r).

Tool developed by Ugo Candido.
Last reviewed for accuracy on: October 25, 2023.