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How To Find the Sum of a Finite Geometric Series

A geometric series is a list of numbers where each number, or term, is found by multiplying the previous term by a common ratio r. If we call the first term a, then the geometric series can be expressed as follows:

sum of finite geometric series: Example of a finite geometric series

We call this a finite geometric series because there is a limited number of terms (an infinite geometric series continues on forever.) In this example, there are 10 terms, the common ratio is r, and each of the terms of the geometric sequence follows the same pattern. The first term is a. The second term is the previous term a multiplied by r. The third term is the second term sum of finite geometric series: The second term in a geometric series multiplied again by r to create sum of finite geometric series: The third tem in a geometric series, and so on until the last term.

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Three Types of Geometric Proofs You Need to Know

geometric proofs: Diagram showing a two column proof

Geometric proofs are given statements that prove a mathematical concept is true. In order for a proof to be proven true, it has to include multiple steps. These steps are made up of reasons and statements.

There are many types of geometric proofs, including two-column proofs, paragraph proofs, and flowchart proofs. We’ll walk you through each type.

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One-to-One Functions: The Exceptional Geometry Rule

one-to-one function: Function F diagram

You need to understand one-to-one functions to grasp other concepts, like inverse functions. But first, let’s start with the definition of a function. A function is a geometric rule that shows a relationship between two sets of numbers. These ordered pairs of numbers are called the domain of the function (the input values) and the range of the function (the output values). In any given function, only one output value can be paired with a given input value.

See Function F below. This set of numbers is a function because no two outputs, or range values, have the same input, or domain values. However, it isn’t a one-to-one function. Let’s explore what this is.

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What Is the Converse of the Pythagorean Theorem?

converse of the pythagorean theorem: types of triangle

The converse of the Pythagorean Theorem tells us that by comparing the sum of the squares of two sides of a triangle to the square of its third side, we can determine whether that triangle is an acute, right, or obtuse.

To review, the Pythagorean Theorem is one of the most famous theorems in trigonometry and helps us determine the sides of a right triangle. Some other formulas you might need for triangle relate to finding the base of a triangle and the area. Here are additional articles on how to find the area of a right triangle and one on how to find the third side of a triangle.

Read on to figure out how the converse of the Pythagorean Theorem works!

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High School Math Help: Find the Perfect Geometry Tutor

Geometry tutor: A student wearing headphones waving during online class

If you're the parent of a high school student and you're looking for a geometry tutor, you've come to the right place. There are many options for finding a tutor, whether you opt for a college-level student majoring in math or you get help from a local teacher.

But selecting a virtual tutor opens up the possibilities of finding a skilled, experienced tutor who can meet your specific needs — you can access tutors worldwide. This is especially important when it comes to high school math, because there are so many important subject areas and concepts within math — including geometry — and having more options can help you choose the best tutor for you.

And, finding a geometry tutor can help your student with test preparation for key exams, including the SAT math portion.

From education qualifications to teaching style, here's what to look for in a geometry tutor, plus how to brush up on concepts between tutoring sessions.

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