### Edexcel GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Triangular Numbers

Triangular numbers are a sequence of numbers that are formed by adding consecutive positive integers. They are called triangular because they can be represented visually as dots arranged in an equilateral triangle.

The first few triangular numbers are:

## Formula for Triangular Numbers

The formula for the nth triangular number is:

Here, represents the nth triangular number, and is the position of the triangular number in the sequence.

### Examples Using the Formula

1. Find the 8th triangular number.

Using the formula with :

2. Find the 20th triangular number.

Using the formula with :

3. Find the 100th triangular number.

Using the formula with :

### Identifying Triangular Numbers

To determine if a given number is a triangular number, we can use the formula and solve for .

4. Is 325 a triangular number?

We want to see if there is an integer value of for which .

By trial and error, we find that , so . Therefore, 325 is indeed a triangular number.

Quizzes