Sort these infinite sequences into groups.

  • How will you choose to define the groups?
  • Are there some sequences which belong to more than one group?

When looking for ways to group the sequences you might ask yourself the following questions.

  • Is each term bigger or smaller than the previous one?

  • How does the difference between adjacent terms change as you go along the sequence?

  • Thinking about a pair of sequences, what is the same and what is different?

  • Can you find a rule for generating the \(n^\text{th}\) term?

You might find it helpful to plot a graph of a sequence to get a feel for how it is behaving.