6 4 6 12 22 ?

Options

A. 26
B. 36
C. 86
D. 66

Explanation

To find the missing number in the series: 6, 4, 6, 12, 22, ?, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the first two numbers: 6 and 4.**
- We can see that 6 is reduced to 4. This can be achieved by subtracting 2 from 6.
- **Calculation:**
\[ 6 - 2 = 4 \]

2. **Next, look at the transition from 4 to 6.**
- To go from 4 to 6, we can add 2 to 4.
- **Calculation:**
\[ 4 + 2 = 6 \]

3. **Now, analyze the transition from 6 to 12.**
- To get from 6 to 12, we can double 6 and subtract 0.
- **Calculation:**
\[ 6 \times 2 = 12 \]

4. **Next, observe the transition from 12 to 22.**
- To go from 12 to 22, we can add 10 to 12.
- **Calculation:**
\[ 12 + 10 = 22 \]

5. **Now, we need to find the next number after 22.**
- Following the pattern, we can divide 22 by 2 and then add the next square number.
- **Calculation:**
\[ 22 \div 2 = 11 \]
- The next square number after \(2^2\) and \(3^2\) is \(4^2 = 16\).
- **Final Calculation:**
\[ 11 + 25 = 36 \]

Thus, the missing number in the series is **36**.