189, 188, 185, 178, 163, ?

Options

A. 130
B. 134
C. 136
D. 132

Explanation

To solve the series: 189, 188, 185, 178, 163, ?, we will analyze the differences between the consecutive terms.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 189, 188, 185, 178, 163.

2. **Calculate the differences**:
- The difference between the first two terms:
\( 189 - 188 = 1 \)
- The difference between the second and third terms:
\( 188 - 185 = 3 \)
- The difference between the third and fourth terms:
\( 185 - 178 = 7 \)
- The difference between the fourth and fifth terms:
\( 178 - 163 = 15 \)

So, the differences are: 1, 3, 7, 15.

3. **Analyze the differences**:
- The differences themselves form a series: 1, 3, 7, 15.
- Let's calculate the differences of these differences:
- \( 3 - 1 = 2 \)
- \( 7 - 3 = 4 \)
- \( 15 - 7 = 8 \)

The second level differences are: 2, 4, 8.

4. **Identify the pattern in the second level differences**:
- The second level differences are doubling: \( 2 \times 2 = 4 \), \( 4 \times 2 = 8 \).
- Thus, the next second level difference should be \( 8 \times 2 = 16 \).

5. **Calculate the next first level difference**:
- The next first level difference will be:
\( 15 + 16 = 31 \).

6. **Find the next term in the original series**:
- The next term in the series will be:
\( 163 - 31 = 132 \).

7. **Final answer**:
- Therefore, the next number in the series is **132**.