Question

Find the next 3 numbers in this series and explain the pattern: 9, 4, 1, 0, ...

a) -1, -4, -9
b) -16, -25, -36
c) 16, 25, 36
d) 1, 8, 27

Answer 1

The next three numbers in the series are 1, 4, and 9, following the pattern of square numbers. The pattern involves taking the square of the descending integers, including the negatives.

Step-by-step explanation:

To find the next three numbers in the series 9, 4, 1, 0, we need to identify the pattern. Looking at the series, we can see that each number is a square of an integer, decreasing each time: 9 is 3², 4 is 2², 1 is 1², and 0 is 0². Following this pattern, the next three numbers would be the squares of negative integers: (-1)², (-2)², and (-3)².

Therefore, the next three numbers in the series are:

1. 1 (which is (-1)²)
2. 4 (which is (-2)²)
3. 9 (which is (-3)²)

The correct answer is d) 1, 8, 27. These numbers reflect the sequence of squares for negative numbers. Since the student's question involved simple arithmetic patterns, the subject area is Mathematics, and the problem itself is typically studied at the Middle School level.