Final answer:
The next number in the sequence 3600, 900, 400, 225 is 144, found by identifying and continuing the pattern of square ratios between the numbers.
Step-by-step explanation:
To find the next number in the sequence 3600, 900, 400, 225, we need to look for a pattern in the changes between the numbers. The ratios between the consecutive numbers are 3600:900 = 4:1, 900:400 = 9:4, and 400:225 = 16:9, which are squares of 2:1, 3:2, and 4:3, respectively.
Predicting the next ratio as the square of 5:4, we calculate the next number by dividing 225 by (5/4)², resulting in the next number in the sequence being 144.