Complete the following numerical series.
`20, 32, 46, 64, 84, 108,` ____________?

Options

A. 134
B. 113
C. 136
D. 128

Answer

To solve the numerical series: `20, 32, 46, 64, 84, 108, ?`, let's analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the differences between consecutive terms:**
- 32 - 20 = 12
- 46 - 32 = 14
- 64 - 46 = 18
- 84 - 64 = 20
- 108 - 84 = 24

So, the differences are: 12, 14, 18, 20, 24.

2. **Identify the pattern in the differences:**
- The differences themselves are increasing:
- 14 - 12 = 2
- 18 - 14 = 4
- 20 - 18 = 2
- 24 - 20 = 4

The pattern in the differences is alternating between adding 2 and 4.

3. **Continue the pattern:**
- The last difference we calculated was 24, which came from adding 4 to the previous difference of 20.
- Following the established pattern, the next difference should be 24 + 2 = 26.

4. **Add the next difference to the last term:**
- Now, add this difference to the last term in the series:
- 108 + 26 = 134.

Thus, the next number in the series is **134**.

### Final Answer:
The next number in the series is **134**.