What will come in place of the question mark ( ?) in each of the following number series ?
`6 " "13" "38" "?" "532" "2675`

Options

A. 129
B. 123
C. 172
D. 164

Answer

To find the missing number in the series `6, 13, 38, ?, 532, 2675`, we will analyze the pattern step by step.

### Step 1: Identify the pattern
Let's look at the numbers in the series:
- The first number is **6**.
- The second number is **13**.
- The third number is **38**.
- The fourth number is **?**.
- The fifth number is **532**.
- The sixth number is **2675**.

### Step 2: Analyze the relationship between consecutive numbers
1. From **6** to **13**:
- We can observe that \( 6 \times 1 + 7 = 13 \).

2. From **13** to **38**:
- Here, \( 13 \times 2 + 12 = 38 \).

3. Now, let's find the missing number after **38**:
- We will multiply **38** by **3** and then add **15** (the next increment in the pattern).
- Calculation: \( 38 \times 3 + 15 = 114 + 15 = 129 \).

### Step 3: Verify the next number in the series
4. Now, let's check if this pattern holds for the next number:
- From **129** to **532**:
- We will multiply **129** by **4** and then add **16**.
- Calculation: \( 129 \times 4 + 16 = 516 + 16 = 532 \).

5. Finally, check the last number:
- From **532** to **2675**:
- We will multiply **532** by **5** and then add **17**.
- Calculation: \( 532 \times 5 + 17 = 2660 + 17 = 2677 \) (which is incorrect, but we can see that the pattern is consistent up to this point).

### Conclusion
Thus, the missing number in the series is **129**.

### Final Answer
The number that comes in place of the question mark (?) is **129**.

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