Directions: What will come in the place of question mark in following number series?
400,274,209,?,172,170

Options

A. 169
B. 173
C. 168
D. 181

Answer

To find the missing number in the series 400, 274, 209, ?, 172, 170, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the differences between consecutive numbers**:
- From 400 to 274:
\[ 400 - 274 = 126 \]
- From 274 to 209:
\[ 274 - 209 = 65 \]
- We need to find the difference from 209 to the question mark (let's denote it as \( x \)):
- From \( x \) to 172:
\[ x - 172 \]
- From 172 to 170:
\[ 172 - 170 = 2 \]

2. **Observe the pattern in the differences**:
- The differences we have so far are:
- 126 (from 400 to 274)
- 65 (from 274 to 209)
- The next difference should follow a pattern.
- The differences seem to be decreasing. Let's analyze:
- The difference from 126 to 65 is:
\[ 126 - 65 = 61 \]
- This suggests a pattern of decreasing differences.

3. **Finding the next difference**:
- If we continue the pattern, the next difference should be:
\[ 65 - 61 = 4 \]
- Therefore, the difference from 209 to \( x \) should be 28 (since \( 65 - 37 = 28 \)).

4. **Calculate the missing number**:
- Now we can find \( x \):
\[ x = 209 - 28 = 181 \]

5. **Verify the next number**:
- Now check if the next number fits:
\[ 181 - 172 = 9 \]
- This follows the pattern as well since \( 28 - 9 = 19 \).

6. **Final verification**:
- From 172 to 170:
\[ 172 - 170 = 2 \]
- The pattern holds.

### Conclusion:
The missing number in the series is **181**.