Find the wrong number in the series given below:
13 34 74 170 290 450

Options

A. 74
B. 170
C. 290
D. 450

Answer

To find the wrong number in the series 13, 34, 74, 170, 290, 450, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
The series appears to be generated by the sum of squares of consecutive prime numbers. Let's check each number in the series to see if they fit this pattern.

### Step 2: Calculate the first number
- The first number is **13**.
- It can be expressed as \(2^2 + 3^2 = 4 + 9 = 13\).

### Step 3: Calculate the second number
- The second number is **34**.
- It can be expressed as \(3^2 + 5^2 = 9 + 25 = 34\).

### Step 4: Calculate the third number
- The third number is **74**.
- It can be expressed as \(5^2 + 7^2 = 25 + 49 = 74\).

### Step 5: Calculate the fourth number
- The fourth number is **170**.
- It can be expressed as \(7^2 + 11^2 = 49 + 121 = 170\).

### Step 6: Calculate the fifth number
- The fifth number is **290**.
- It can be expressed as \(11^2 + 13^2 = 121 + 169 = 290\).

### Step 7: Calculate the sixth number
- The sixth number is **450**.
- We need to check if it can be expressed as the sum of squares of the next two prime numbers, which are 13 and 17.
- \(13^2 + 17^2 = 169 + 289 = 458\).

### Step 8: Identify the wrong number
- Since \(450\) does not equal \(458\), the number **450** is incorrect in the series.

### Conclusion
The wrong number in the series is **450**.

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