What wil come in the place of question mark in following number series:
400,274,209,181,172,?

Options

A. 169
B. 173
C. 168
D. 170

Answer

To solve the number series: 400, 274, 209, 181, 172, ?, we will analyze the differences between consecutive terms to identify a pattern.

### Step 1: Identify the series
The series given is:
- 400
- 274
- 209
- 181
- 172
- ?

### Step 2: Calculate the differences between consecutive terms
Let's calculate the differences:
1. Difference between 400 and 274:
\[ 400 - 274 = 126 \]
2. Difference between 274 and 209:
\[ 274 - 209 = 65 \]
3. Difference between 209 and 181:
\[ 209 - 181 = 28 \]
4. Difference between 181 and 172:
\[ 181 - 172 = 9 \]

Now we have the differences:
- 126
- 65
- 28
- 9

### Step 3: Analyze the differences
The differences are:
- 126
- 65
- 28
- 9

Now, let's look for a pattern in these differences:
1. The difference between 126 and 65:
\[ 126 - 65 = 61 \]
2. The difference between 65 and 28:
\[ 65 - 28 = 37 \]
3. The difference between 28 and 9:
\[ 28 - 9 = 19 \]

Now we have the second set of differences:
- 61
- 37
- 19

### Step 4: Analyze the second set of differences
Now, let's look for a pattern in the second set of differences:
1. The difference between 61 and 37:
\[ 61 - 37 = 24 \]
2. The difference between 37 and 19:
\[ 37 - 19 = 18 \]

The differences are:
- 24
- 18

### Step 5: Predict the next difference
We can see that the differences are decreasing. If we continue this pattern, the next difference could be:
\[ 19 - 10 = 9 \]
This suggests that the next difference could be 9.

### Step 6: Calculate the next term
Now, we can calculate the next term in the series:
\[ 172 - 9 = 163 \]

### Conclusion
The next term in the series is **163**.