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# Geometric Sequence Calculator with Graph Feature

Geometric Sequence Calculator
 First term of the sequence (a1): Common ratio (r): Enter n: Precision: 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 900 1000

Embed Geometric Sequence Calculator Widget

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:

an = a1rn-1

Where:

1. an is the nth term.
2. a1 represents the first term.
3. r stands for the common ratio.
4. n is the position of the term in the sequence.

For instance, in a sequence where the first term a1 is 2 and the common ratio r is 3, the 7th term can be calculated as:

a7= 2 × 3(7-1) = 1458

The sum of the first 7 terms Sn = a1 + ...+ an = 2 * (1 - 37) /(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

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