squares nth term

some sequences, presented out of sequence!
that are fairly easy to generalise
and 'see' from the diagrams how the general rule is formed

and, also
the general rules all factorise
and the diagrams can all be re-formed (by cutting and fitting) to make rectangles
so the two forms of general rules (nth terms) can be related

students form a growing sequence for each question and maybe describe it
(what will e.g. the 11th or 23rd shape in the pattern look like?)

they can then find an nth term rule
and hopefully justify this in relation to the diagram

can they make a rectangle out of the squares for each question?
and form an alternative generalisation?

how are the two generalisations the same (equivalent)?