What is the next number in the sequence 225, 100, 36, 9, 1 ?(a) -7(b) -6(c) 0(d) -1

To find the next number in the sequence 225, 100, 36, 9, 1, let us analyze the pattern:

1. **Identify the relationship between consecutive terms**:
- First term: 225
- Second term: 100
The difference is \( \sqrt{225} = 15 \) and \( \sqrt{100} = 10 \).
- Third term: 36
The difference is \( \sqrt{100} = 10 \) and \( \sqrt{36} = 6 \).
- Fourth term: 9
The difference is \( \sqrt{36} = 6 \) and \( \sqrt{9} = 3 \).
- Fifth term: 1
The difference is \( \sqrt{9} = 3 \) and \( \sqrt{1} = 1 \).

The pattern suggests that each number is a perfect square, decreasing such that the square roots form the sequence: \( 15, 10, 6, 3, 1 \).

2. **Predict the next square root**:
The sequence of square roots decreases by:
\( 15 - 10 = 5, \, 10 - 6 = 4, \, 6 - 3 = 3, \, 3 - 1 = 2 \).
The next difference will be \( 1 - 1 = 1 \), so the next square root is \( 1 - 1 = 0 \).

3. **Find the next number**:
The square of 0 is \( 0^2 = 0 \).

**Answer**: The next number in the sequence is (c) 0.