Why can an arithmetic series never converge to a finite sum?

1. A series converges when its running total settles closer and closer to one fixed value. 2. In an arithmetic sequence the terms never shrink towards zero, because the same constant is added each time. 3. Adding terms that do not shrink keeps pushing the total further out. 4. So the total heads off to positive or negative infinity and no limit exists. 5. Some geometric series do converge, because their terms can shrink towards zero. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_