Question

Write a paragraph that explains why the numbers found in Problem 103 are called triangular.

Short answer

$1,3,6,10,15,21\mathrm{and}28$ all these numbers are triangular numbers.

Step-by-step solution

Step 1. Write the given information.

The given information is:

Write a paragraph that explains why the numbers found in Problem 103 are called triangular.

Step 2. Write about triangular numbers.

A number that can be represented by a pattern of dots and arranged in an equilateral triangle with the same number of dots on each, is known as a triangular number.

In problem 103, we had calculated seven numbers $1,3,6,10,15,21\mathrm{and}28$, these numbers are called triangular because an equilateral triangle can be formed by each of these numbers.

We can also say that triangular numbers are obtained by adding a next natural number in the previously obtained number of a sequence.

$$\begin{gathered} 1=1 \\ 3=1+2 \\ 6=1+2+3 \\ 10=1+2+3+4 \\ 15=1+2+3+4+5 \\ 21=1+2+3+4+5+6 \\ 28=1+2+3+4+5+6+7 \end{gathered}$$