Find the missing number
2, 3, 7, _______, 2112

Options

A. 36
B. 45
C. 46
D. 49

Answer

To find the missing number in the sequence 2, 3, 7, ____, 2112, we will analyze the pattern in the sequence.

### Step 1: Identify the pattern
We start with the first number, which is 2. We will look for a relationship between the numbers.

### Step 2: Calculate the second number
The second number is 3. We can express this as:
\[ 2^2 - 1 = 4 - 1 = 3 \]

### Step 3: Calculate the third number
The third number is 7. We can express this as:
\[ 3^2 - 2 = 9 - 2 = 7 \]

### Step 4: Find the missing number
Now we need to find the missing number, which we will denote as \( x \). Using the pattern we have established:
\[ 7^2 - 3 = 49 - 3 = 46 \]
So, the missing number is 46.

### Step 5: Calculate the next number
Now, we need to verify that this pattern continues to the last number, which is 2112:
\[ 46^2 - 4 = 2116 - 4 = 2112 \]

### Conclusion
Thus, the missing number in the sequence is **46**.

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