Arithmetic Series Question

[abstract sand]

what are we supposed to calculate

[tidal hare]

If you want to know the next in the series then i think it should be
9×14/5×21

[ancient temple]

but my worksheet says its arithmetic

[ancient temple]

the common difference and next number i guesss

[hallow condor]

Well, if the first term has index 1, then its seems that a(n) has the following formula:
a(n) = (2n + 1)(3n + 2)/((n + 1)(6n - 3))
This isn't an arithmetic series, of course.

[ancient temple]

bruh worksheet wrong