# Geometric Sequence Calculator with Graph Feature

## About Geometric Sequence Calculator

Discover the world of mathematical progressions with our high-precision Geometric Sequence Calculator. Not only can you calculate the nth term and the sum of the first n terms of a geometric sequence with full step-by-step solution, but you can also visualize the progression with our integrated graph feature.

## What Is a Geometric Sequence?

In the realm of mathematics, a geometric sequence, also known as a geometric progression, is a sequence of numbers where each term after the initial one is derived by multiplying the preceding term by a fixed, non-zero number termed the "common ratio." This unique characteristic sets geometric sequences apart from other mathematical sequences.

## How to Calculate a Geometric Sequence?

If you're looking to find the nth term of a geometric sequence, the formula is:

a_{n} = a_{1}r^{n-1}

Where:

- a
_{n}is the nth term. - r stands for the common ratio.
- n is the position of the term in the sequence.

_{1}represents the first term.

For instance, in a sequence where the first term a_{1} is 2 and the common ratio r is 3, the 7th term can be calculated as:

a_{7}= 2 × 3^{(7-1)} = **1458**

The sum of the first 7 terms S_{n} = a_{1} + ...+ a_{n} = 2 * (1 - 3^{7}) /(1 - 3) = **2186**

This mathematical concept has vast applications, especially in fields that involve exponential growth or decay, such as finance and biology.

## FAQ

A geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by a constant ratio. A geometric series, on the other hand, is the sum of the terms of a geometric sequence.

The common ratio of a geometric sequence can be determined by dividing any term in the sequence by its preceding term.

## Reference

Reference this content, page, or tool as:

"Geometric Sequence Calculator" at https://miniwebtool.com/geometric-sequence-calculator/ from miniwebtool, https://miniwebtool.com/

by miniwebtool team. Updated: Oct 03, 2023