Answer: Weeding and feeding can usually be done at the same time, many products are available to do both at once. Weeding will prevent the lawn seed from germinating, and a high nitrogen fertilizer may be too strong for new grass. (Be sure to read and follow the label instructions of whatever you use.)
The best time to seed or overseed a lawn is in the fall so the new grass has time to become established from the roots before it is pressured to grow fast the following spring.
Fall is also a good time to fertilize moderately, it is when the grass plants are building their root reserves. In spring, then, a lesser amount of fertilizer could be applied if a quicker greening is desired.
Core areation is done occasionally if needed to combat soil compaction or to help incorporate additional organic matter in the soil. It is a bit stressful to existing plants since it pulls out plugs of lawn, so it would not be done to a newly seeded area.
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