in the following number series only one is wrong . Find out the wrong number .
`5" "7" "16" "57" "244" "1245" "7506`

Options

A. 7
B. 16
C. 57
D. 244

Answer

To find the wrong number in the series `5, 7, 16, 57, 244, 1245, 7506`, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
We will look at how each number relates to the previous number. The hint from the video suggests that there is a multiplication and addition pattern involving squares.

### Step 2: Check the first number
Starting with the first number:
- The first number is **5**.
- If we multiply **5** by **1** and add **1^2** (which is 1), we get:
\[ 5 \times 1 + 1^2 = 5 + 1 = 6 \]
This means the next number should be **6** instead of **7**.

### Step 3: Check the second number
Now, let's check the second number:
- If we take **6** (the corrected number) and multiply it by **2** and add **2^2** (which is 4):
\[ 6 \times 2 + 2^2 = 12 + 4 = 16 \]
This matches the third number, which is **16**.

### Step 4: Check the third number
Next, we check the third number:
- For **16**, multiply by **3** and add **3^2** (which is 9):
\[ 16 \times 3 + 3^2 = 48 + 9 = 57 \]
This matches the fourth number, which is **57**.

### Step 5: Check the fourth number
Now, check the fourth number:
- For **57**, multiply by **4** and add **4^2** (which is 16):
\[ 57 \times 4 + 4^2 = 228 + 16 = 244 \]
This matches the fifth number, which is **244**.

### Step 6: Check the fifth number
Next, check the fifth number:
- For **244**, multiply by **5** and add **5^2** (which is 25):
\[ 244 \times 5 + 5^2 = 1220 + 25 = 1245 \]
This matches the sixth number, which is **1245**.

### Step 7: Check the sixth number
Finally, check the sixth number:
- For **1245**, multiply by **6** and add **6^2** (which is 36):
\[ 1245 \times 6 + 6^2 = 7470 + 36 = 7506 \]
This matches the seventh number, which is **7506**.

### Conclusion
After checking all the numbers, we find that the second number **7** is incorrect. It should be **6**.

### Final Answer
The wrong number in the series is **7**, and it should be replaced with **6**.

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