Patterns in Mathematics - Relation to Number Sequences

A number pattern is a sequence of numbers that follows a specific rule. For example, in the sequence $2, 4, 6, 8, \dots$, each number increases by $2$.

The position of a number in a sequence is often denoted by $n$. The first term is at $n=1$, the second at $n=2$, and so on.

A common rule in Grade 6 involves finding the $n^{th}$ term by relating the position $n$ to the value of the term. For example, if the sequence is $5, 10, 15, \dots$, the rule is $5 \times n$.

Patterns can be observed in geometric shapes made of matchsticks. If one triangle requires $3$ sticks and two triangles (sharing one side) require $5$ sticks, the pattern follows the rule $2n + 1$.

Square numbers are patterns formed by multiplying a number by itself: $1, 4, 9, 16, \dots$ which is represented as $n^2$ or $n \times n$.

Triangular numbers are numbers that can form an equilateral triangle: $1, 3, 6, 10, \dots$.