Final answer:
The next number in the sequence 1, 4, 9, 16, 25, ... is 36, as it is a list of perfect squares with 36 being the square of 6.
Step-by-step explanation:
The Next Number in the SequenceThe next number in the sequence 1, 4, 9, 16, 25, ... is 36.Explanation of the SequenceThis sequence is a list of perfect squares. Each term in the sequence is the square of its position in the sequence, starting with 1 (1² = 1), 2 (2² = 4), 3 (3² = 9), and so on. Therefore, since 25 is the square of 5, the next term is the square of 6, which is 36.
These numbers are called perfect squares because they are the product of an integer multiplied by itself. Recognizing patterns in sequences is a key skill in mathematics, as it allows us to predict subsequent numbers or terms.The pattern in the sequence 1, 4, 9, 16, 25, ... is that each number is the square of a consecutive positive integer. So, the next number in the sequence is 36, which is 6 squared.