In the number series given below, one number is missing. Each series is followed by four alternatives (1), (2), (3), and (4). One of them is the right answer. Identify and indicate it as per the "instructions".
13,74,290,650....

Options

A. 1248
B. 1370
C. 1346
D. 1452

Answer

To solve the missing number in the series 13, 74, 290, 650, we will identify the pattern in the series step by step.

### Step 1: Identify the Pattern
The series appears to involve prime numbers and their squares. Let's analyze the first few terms:

1. **First term (13)**:
- \(2^2 + 3^2 = 4 + 9 = 13\)

2. **Second term (74)**:
- \(5^2 + 7^2 = 25 + 49 = 74\)

3. **Third term (290)**:
- \(11^2 + 13^2 = 121 + 169 = 290\)

4. **Fourth term (650)**:
- \(17^2 + 19^2 = 289 + 361 = 650\)

### Step 2: Determine the Next Term
Now, we need to find the next term in the series. Following the established pattern:

- The next prime numbers after 19 are 23 and 29.
- Calculate \(23^2 + 29^2\):
- \(23^2 = 529\)
- \(29^2 = 841\)

Now, add these two squares:
\[ 529 + 841 = 1370 \]

### Conclusion
Thus, the missing number in the series is **1370**.

### Final Answer
The missing number is **1370**.