In this Khan Academy activity, students will determine which sequence, arithmetic or geometric, fits a word problem.

The purpose of this task is for students to explicitly consider when a discrete or continuous model
is appropriate for a given context. The situations in this task are designed to contrast discrete and
continuous models for both linear and exponential functions. The task also provides opportunity
for students to model with mathematics by connecting the type of change, either linear or
exponential with the nature of that change, either discrete or continuous.

This task introduces a decreasing arithmetic sequence to further solidify the idea that
arithmetic sequences have a constant difference between consecutive terms. Again, connections
should be made among all representations: table, graph, recursive and explicit formulas. The
emphasis should be on comparing increasing and decreasing arithmetic sequences through the
various representations.

The purpose of this task is to practice writing recursive and explicit formulas for
arithmetic and geometric sequences from a table. This task also provides practice in using tables to
identify when a sequence is arithmetic, geometric, or neither. The task extends students’
experiences with sequences to include geometric sequences with alternating signs, and more work
with fractions and decimal numbers in the sequences.