(1) The lengths of the sides of a right triangle are three consecutive terms of
an increasing arithmetic sequence. Show that the lengths are in the ratio 3:4:5.
The first three terms of an arithmetic sequence are: .
If they are the sides of a righ triangle: .
. . which simplifies to: .
. . which factors: .
. . and has the positive root: .
Hence, the three sides are: .
And their ratio is: .
(3) Find and if the sequence is geometric.
The first four terms of a geomeric sequence are: .
So we have: .
Equate  and : .
Substiute into : .
Substitute into : .