An arithmetic sequence adds a fixed amount each step; a geometric one multiplies by a fixed factor. Why does that difference make geometric growth eventually overtake any arithmetic sequence, however large its common difference?

A. Because a fixed step is eventually outpaced by one that keeps growing.

The arithmetic sequence adds d at step 5 and at step 5000; the geometric one adds a proportion of its current value, so its increment grows exactly as fast as it does. Take 1000n against 2ⁿ: the arithmetic leads 10,000 to 1024 at n = 10 and trails 20,000 to a million at n = 20. Both are unbounded, the difference is the rate.