Sequences - investigations

Investigate the following situations and identify rules e.g. the n-th ... is ...

• possible rules or hypotheses
• proofs by induction - investigations 1 to 4

Investigation 1

Triangle numbers

Investigation 2

Each person in the room shakes hands with every other person (solutions).

Investigation 3
 

All the diagonals of a convex polygon are drawn.

Investigation 4
 

Using straight lines, a circle is divided into the maximum number of pieces.

Investigation 5
 

Playing cards are used to make a "house of cards".

Investigation 6
 

Tiling patterns are made from green and yellow tiles.

Investigation 7

Tennis balls are arranged in the form of a square-based pyramid.

Investigation 8

Tennis balls are arranged in the form of a tetrahedron.