Providentially tells you how something happened: in a lucky way, as if it were arranged to help. “The rain stopped providentially just as we reached the door.” It is the adverb that belongs with providential, so it carries the same extra feeling as that adjective. People gloss it as luckily, and in loose talk that is fair. Though actually, luckily is lighter and more common. Providentially still hints that the timing was not empty chance — that care, fate, or God had a hand. You will meet it in careful writing and in religious speech more than in the playground. If you only need “it was lucky,” say luckily. Use this word when you want that older, heavier colour.