The algebraic notation for these topics can be quite intimidating at first glance.
To help students understand how recursive formulas work, give them some think-time to complete the included informal introduction here. Once students understand how arithmetic and geometric sequences "behave", introduce the algebraic notation to formalize the patterns.
Also included here is a graphic organizer including explicit and recursive formulas for arithmetic and geometric sequences.
I hope these resources supplement your students' studies of sequences! Sample keys are included for your convenience.