Finding Quadratic Number Patterns

Patterns are one of the fundamental subjects of mathematics. Therefore, it has an important place in mathematics teaching. It is started by explaining to the students with repetitive shapes from preschool or first grade. In the first years when students meet the patterns, they concentrate on the processes of continuing and finding the missing ones. Algebraic representation of general rules is also taught, as abstraction skills begin to increase from the seventh grade.
Patterns are numbers, shapes, etc., created according to a certain rule, logic are series. Patterns with a constant increment are called arithmetic sequences. Finding the rules for 1st order patterns is easy. It's really hard to find rules for 2nd order patterns.