What will come in place of question mark (? ) in the following number series ?
निम्नलिखित संख्या श्रंखला में प्रश्नवाचक चिन्ह (?) के स्थान पर क्या आयेगा ?
`62 " "87 " "187 " "412 " "812" "?`

Options

A. 1012
B. 1437
C. 1337
D. 1457

Answer

To solve the number series: 62, 87, 187, 412, 812, ?, we will analyze the differences between the consecutive numbers and identify a pattern.

### Step 1: Find the differences between consecutive terms.
- Difference between 87 and 62:
\[ 87 - 62 = 25 \]
- Difference between 187 and 87:
\[ 187 - 87 = 100 \]
- Difference between 412 and 187:
\[ 412 - 187 = 225 \]
- Difference between 812 and 412:
\[ 812 - 412 = 400 \]

### Step 2: List the differences found.
The differences are:
- 25
- 100
- 225
- 400

### Step 3: Identify a pattern in the differences.
Now, let's analyze the differences:
- 25 = \(5^2\)
- 100 = \(10^2\)
- 225 = \(15^2\)
- 400 = \(20^2\)

We can see that the differences correspond to the squares of multiples of 5:
- \(5^2\), \(10^2\), \(15^2\), \(20^2\)

### Step 4: Predict the next difference.
Following the pattern, the next difference should be:
- \(25^2 = 625\)

### Step 5: Add the next difference to the last term in the series.
Now, we will add this difference to the last term in the series (812):
\[ 812 + 625 = 1437 \]

### Conclusion:
The number that will come in place of the question mark (?) in the series is **1437**.

---