Final answer:
When the period of a variable star increases, the time it takes for the star to go through one complete cycle of brightness changes increases. This means that the frequency of the brightness changes decreases.
Step-by-step explanation:
When the period of a variable star increases, it means that the time it takes for the star to go through one complete cycle of brightness changes has increased. If the period increased 2.5 times, then it now takes 2.5 times longer for the star to go from maximum brightness to minimum brightness and back to maximum brightness again.
The frequency of the brightness changes of the star is inversely related to its period. In other words, as the period increases, the frequency decreases. Since the period of the star increased 2.5 times, the frequency of its brightness changes decreased by the same amount.
For example, if the star originally had a period of 10 days (meaning it took 10 days to go through one complete cycle of brightness changes), and the period increased 2.5 times, the new period would be 25 days. So, the frequency of the brightness changes decreased from 1 change every 10 days to 1 change every 25 days.