5 6 14 45 ?

Options

A. 183
B. 185
C. 138
D. 184

Explanation

To find the missing number in the series 5, 6, 14, 45, we will analyze the pattern step by step.

### Step 1: Identify the Pattern
We start with the given series: 5, 6, 14, 45.

### Step 2: Analyze the Transition Between Numbers
- From 5 to 6:
- We can see that 5 multiplied by 1 plus 1 gives us 6.
- Calculation: \( 5 \times 1 + 1 = 6 \)

- From 6 to 14:
- Now, we take 6 multiplied by 2 plus 2.
- Calculation: \( 6 \times 2 + 2 = 12 + 2 = 14 \)

- From 14 to 45:
- Next, we take 14 multiplied by 3 plus 3.
- Calculation: \( 14 \times 3 + 3 = 42 + 3 = 45 \)

### Step 3: Apply the Identified Pattern to Find the Next Number
Now, we will apply the same pattern to find the next number after 45:
- We take 45 multiplied by 4 plus 4.
- Calculation: \( 45 \times 4 + 4 = 180 + 4 = 184 \)

### Conclusion
Thus, the missing number in the series is **184**.

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