Which year marks the centennial celebration of the Army?

The centennial celebration of the Army marks 100 years since its establishment, which traces back to the year 1775. This is significant as it commemorates the founding of the Continental Army, created by the Second Continental Congress on June 14, 1775, during the American Revolutionary War. Celebrating a centennial emphasizes the historical importance and impact of the Army's formation in shaping the nation.

The other options do not align with the correct timeline. For instance, 1875 represents a time well past the Army's founding, while 1975 would mark the bicentennial establishment rather than the centennial. Lastly, 2075 is far into the future, which would not be relevant to the context of the centennial celebration in historical discussions concerning the Army's legacy.