The test that tells them apart
Subtract each term from the one after it. If that difference is the same every time, it's an arithmetic sequence — 2, 5, 8, 11 has a constant difference of 3. Divide each term by the one before it instead, and if that ratio is the same every time, it's a geometric sequence — 2, 6, 18, 54 has a constant ratio of 3. A sequence can satisfy one test or the other, but a genuine arithmetic sequence (with a nonzero common difference) never also satisfies the ratio test, and vice versa.
A worked example starting from the same number
Start both sequences at 3, using 4 as the common difference for one and the common ratio for the other. Arithmetic (add 4 each time) runs 3, 7, 11, 15, 19, 23 — the 6th term is only 23. Geometric (multiply by 4 each time) runs 3, 12, 48, 192, 768, 3072 — the 6th term is already 3,072. Both sequences start identically and grow by "4" in some sense at every step, but arithmetic growth stays linear while geometric growth compounds, so the gap between them widens quickly rather than staying proportional.
Why the difference matters beyond the test itself
The same distinction shows up anywhere a quantity changes by a fixed amount versus a fixed percentage — a savings plan that adds a flat ₹1,000 every month behaves arithmetically, while an investment compounding at a fixed rate behaves geometrically. Recognizing which pattern applies is what tells you whether to reach for the nth-term formula that adds (arithmetic) or the one that multiplies (geometric) — covered with worked examples for both in the companion article on finding the nth term of a sequence.
What if a sequence passes neither test?
Plenty of well-known sequences are neither arithmetic nor geometric — the Fibonacci sequence (1, 1, 2, 3, 5, 8, ...) is the most famous example, since neither its differences nor its ratios stay constant. It still isn't random, though — see the companion article on why Fibonacci ratios approach the golden ratio for what pattern it follows instead.