What would be the next two numbers In the following series ?
`2,3,5,9,8,27,11,?,? `

Options

A. `14,729`
B. `15,81`
C. `81,14`
D. `14,728`

Answer

To find the next two numbers in the series `2, 3, 5, 9, 8, 27, 11, ?, ?`, we can break the series into two distinct sequences.

### Step-by-Step Solution:

1. **Identify the two separate sequences**:
- The first sequence consists of the numbers at the 1st, 3rd, 5th, and 7th positions: `2, 5, 8, 11`.
- The second sequence consists of the numbers at the 2nd, 4th, and 6th positions: `3, 9, 27`.

2. **Analyze the first sequence**:
- The first sequence is `2, 5, 8, 11`.
- The pattern here is that each number increases by 3:
- \(5 - 2 = 3\)
- \(8 - 5 = 3\)
- \(11 - 8 = 3\)
- Therefore, the next number in this sequence would be:
- \(11 + 3 = 14\)

3. **Analyze the second sequence**:
- The second sequence is `3, 9, 27`.
- The pattern here is that each number is multiplied by 3:
- \(9 = 3 \times 3\)
- \(27 = 9 \times 3\)
- Therefore, the next number in this sequence would be:
- \(27 \times 3 = 81\)

4. **Combine the results**:
- The next two numbers in the series are `14` and `81`.

### Final Answer:
The next two numbers in the series are **14** and **81**.