Free Printable Graphing Sequences Worksheets for Grade 9

In 9th grade or Algebra 1, the focus is on solidifying the connection between sequences and function families. Students explicitly link arithmetic sequences to linear functions and geometric sequences to exponential functions, often using recursive and explicit formulas to describe them.

Give students an explicit formula, like a(n) = 3n + 2, and have them generate the first few terms and graph them. Then, have them graph the related continuous function, y = 3x + 2. This visual comparison makes it clear that the sequence's graph is a set of discrete points that fall on the line of the corresponding function.

Students may struggle with the notation, particularly for recursive formulas where a term is defined by the preceding term. They may also find it difficult to write an explicit formula when given a graph, which requires them to identify the starting value and the common difference or ratio from the visual pattern.

This worksheet can be assigned as an interactive digital quiz on the Wayground platform, providing students with immediate feedback. For review or assessment, every worksheet includes a complete answer key, which is accessible for both the digital and printable PDF versions.

This topic is a key part of the Common Core High School Functions standards. It formally establishes sequences as functions whose domain is a subset of the integers (HSF-IF.A.3). It also provides a foundational context for constructing linear and exponential functions from arithmetic and geometric sequences, respectively (HSF-LE.A.2).

Challenge advanced students by asking them to work backward. Provide them with a graph of a sequence and have them derive both the recursive and explicit formulas. You can also ask them to find the value of a much later term (e.g., the 50th term), forcing them to use the explicit formula rather than just extending the pattern.