Find the missing (?) in the series 50, 49.5, ?, 45.5, 42, 37.5, .......
A. 49
B. 48
C. 47.5
D. 46

Options

A. D
B. B
C. A
D. C

Answer

To find the missing number in the series 50, 49.5, ?, 45.5, 42, 37.5, we can analyze the differences between the consecutive terms.

1. **Identify the given series**:
- The series is: 50, 49.5, ?, 45.5, 42, 37.5.

2. **Calculate the differences between the known terms**:
- The difference between 50 and 49.5 is:
\[ 50 - 49.5 = 0.5 \]
- The difference between 49.5 and 45.5 is not known yet, so we will denote it as \( x \).
- The difference between 45.5 and 42 is:
\[ 45.5 - 42 = 3.5 \]
- The difference between 42 and 37.5 is:
\[ 42 - 37.5 = 4.5 \]

3. **Analyze the pattern of differences**:
- The first difference is 0.5.
- The second difference (from 49.5 to 45.5) is \( x \).
- The third difference is 3.5.
- The fourth difference is 4.5.

4. **Determine the pattern in the differences**:
- The differences appear to be increasing. The difference from 45.5 to 42 (3.5) is less than the difference from 42 to 37.5 (4.5).
- If we assume that the differences are increasing by 1 each time, we can set up:
- First difference: 0.5
- Second difference: 1.5 (to find the missing number)
- Third difference: 2.5 (from 45.5 to 42)

5. **Calculate the missing number**:
- If we subtract 1.5 from 49.5, we can find the missing number:
\[ 49.5 - 1.5 = 48 \]

6. **Verify the differences**:
- Now, let's check the difference from 48 to 45.5:
\[ 48 - 45.5 = 2.5 \]
- The difference from 45.5 to 42 is 3.5, and from 42 to 37.5 is 4.5, confirming our pattern.

Thus, the missing number in the series is **48**.