Though the sun appears to have a steady brightness, its luminosity actually undergoes (A)/ undergo (B) changes over time.
A film that the scientists made out of a sequence (A) / Sequel (B) of hundreds of white light images shows how the sunspots appear and disappear periodically over an eleven-year cycle.
Perched (A) / Parched (B) on top of a thickly – wooded hill, the five tribal hamlets have been inaccessible for decades.
Luminosity is singular, hence, undergoes is the correct word. Sequence - A set of things next to each other in a set order; a series Sequel - A narrative that is written after another narrative set in the same universe, especially a narrative that is chronologically set after its predecessors, or (perhaps improper usage) any narrative that has a preceding narrative of its own. Perched – settled on something high or narrow. Parched – extremely thirsty