13, 24, 46, 90, 178, ….

Options

A. 354
B. 266
C. 364
D. 344

Explanation

To solve the series 13, 24, 46, 90, 178, ..., we will analyze the differences between consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Identify the Series:**
The given series is: 13, 24, 46, 90, 178.

2. **Calculate the First Differences:**
We will find the differences between consecutive terms:
- 24 - 13 = 11
- 46 - 24 = 22
- 90 - 46 = 44
- 178 - 90 = 88

So, the first differences are: 11, 22, 44, 88.

3. **Calculate the Second Differences:**
Now, we will find the differences of the first differences:
- 22 - 11 = 11
- 44 - 22 = 22
- 88 - 44 = 44

The second differences are: 11, 22, 44.

4. **Calculate the Third Differences:**
Next, we will find the differences of the second differences:
- 22 - 11 = 11
- 44 - 22 = 22

The third differences are: 11, 22.

5. **Identify the Pattern:**
We can see that the first differences are doubling each time:
- 11, 22, 44, 88 (which is 11 * 2^0, 11 * 2^1, 11 * 2^2, 11 * 2^3)

Following this pattern, the next difference should be:
- 88 * 2 = 176.

6. **Calculate the Next Term:**
Now, we add this new difference to the last term in the series:
- 178 + 176 = 354.

7. **Conclusion:**
Therefore, the next term in the series is **354**.

### Final Answer:
The missing figure in the series is **354**.