What will come in the place of question mark (?) in the given number series ?
38, 343, 5489, 137226 ?

Options

A. `4940137`
B. `4040135`
C. `2195617`
D. `2561917`

Answer

To solve the number series: 38, 343, 5489, 137226, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the first term and its operation**:
- The first term is 38.
- The operation to get the second term (343) is:
\[ 38 \times 9 + 1 = 342 + 1 = 343 \]

2. **Identify the second term and its operation**:
- The second term is 343.
- The operation to get the third term (5489) is:
\[ 343 \times 16 + 1 = 5488 + 1 = 5489 \]

3. **Identify the third term and its operation**:
- The third term is 5489.
- The operation to get the fourth term (137226) is:
\[ 5489 \times 25 + 1 = 137225 + 1 = 137226 \]

4. **Identify the pattern**:
- The multipliers are consecutive square numbers:
- \(3^2 = 9\)
- \(4^2 = 16\)
- \(5^2 = 25\)
- The next multiplier should be \(6^2 = 36\).

5. **Calculate the next term**:
- We will apply the identified operation to the last term (137226):
\[ 137226 \times 36 + 1 \]
- First, calculate \(137226 \times 36\):
\[ 137226 \times 36 = 4940136 \]
- Now add 1:
\[ 4940136 + 1 = 4940137 \]

Thus, the number that will come in place of the question mark (?) is **4940137**.