Building blocks

## Suggestion

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.