Why can we think of the sequence \(1,1,1,1,...\) as both an arithmetic sequence and a geometric sequence? Are there any other sequences that are both arithmetic and geometric?

Can we find a sequence that fits in the empty parts of this grouping diagram?

Here is another possible grouping. How do you think this one was constructed?

Why do you think our groupings are labelled strictly increasing and strictly decreasing sequences? (It might help to think about increasing and decreasing functions.)

How would the grouping diagram have changed if we had not used the word strictly in our labelling of our groupings?