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It depends. If your

It depends. If your watermelon came from a grocery store, it likely was a hybrid (a cross between two watermelon varieties). In this case, the watermelons that come from that seed may be different from the parent melon and may have inferior characteristics (such as poor quality, taste, etc). Sometimes, something better than the parent might form, but that's rare. If you think your seeds came from a hybrid, and want to just grow the plant to see what develops, good or bad, then continue to grow it.

 

If, on the other hand, you got a watermelon from a farmer's market, and you know that it was an open-pollinated variety (a cross between plants of the same variety), the seeds will likely come true to type, having the same features as the parent. In this case, if you continue to grow the plant, it most likely will produce fruit like the original watermelon (providing it has the proper light, nutrients, water, temperature, etc.).