8,24,12,36,18,54 (..)

Options

A. 27
B. 108
C. 68
D. 72

Answer

To find the next number in the series 8, 24, 12, 36, 18, 54, we can analyze the pattern in the sequence step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- Look at the sequence: 8, 24, 12, 36, 18, 54.
- We can separate the series into two alternating sequences:
- Sequence A: 8, 12, 18 (1st, 3rd, 5th terms)
- Sequence B: 24, 36, 54 (2nd, 4th, 6th terms)

2. **Analyze Sequence A**:
- Sequence A: 8, 12, 18
- The pattern here is an increase of 4, then 6:
- 12 - 8 = 4
- 18 - 12 = 6
- Following this pattern, the next increase should be 8 (4, 6, 8):
- Next term = 18 + 8 = 26

3. **Analyze Sequence B**:
- Sequence B: 24, 36, 54
- The pattern here is an increase of 12, then 18:
- 36 - 24 = 12
- 54 - 36 = 18
- Following this pattern, the next increase should be 24 (12, 18, 24):
- Next term = 54 + 24 = 78

4. **Combine the Results**:
- The next term in the overall series should be from Sequence A since we alternate:
- The next term after 54 in the series is 26.

### Conclusion:
The next number in the series is **26**.