Visual Patterns
For video explanation of some of techniques of finding formulas, see https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-algebraic-thinking/cc-5th-number-patterns/v/relationships-between-patterns
For a written explanation of how to find formulas like these see http://www.mathsisfun.com/algebra/sequences-finding-rule.html
For more visual pattern work, see http://illuminations.nctm.org/Lesson.aspx?id=597
and http://www.visualpatterns.org/