quadratic growing rules (i)

growing in two directions, across and up, (quadratic) sequences

a ppt is here

the growing sequences of shapes
have a quadratic nth term form

general rules can be established from the diagrams directly and also from factor pairs (they can be reformed into a rectangle)

or by other, algebraic methods...

part of the interest in generalising these growing sequences is in relating apparently different rules, from various 'viewings' of particular cases - that seem 'regular'

for example, question (4) above can have various nth term generlisations from different viewings: