As a private math tutor, I get to see how students in pre-calculus learn about arithmetic and geometric sequences and series. That’s arith-me-tic as an adjective with the accent on the third syllable.
My students relate well enough to the traditional financial examples of savings accounts and car loans and to the biological examples of population growth but I like to engage them with more variety. My favourite alternative is to talk about art, specifically perspective drawings.
The image at the top of this post links to a technical description of geometric series but using the example below makes my job much easier.
A bonus of using examples like this is that they can lead to a discussion of computer graphics and then to the broader topic of how relevant mathematical proficiency is to a wide variety careers. Since most of my students are preparing for university, their parents consistently express their appreciation for anything I can do to encourage their children to keep their options open.