What will come in place of the question mark(?) in each of the following number series ?
20 29 54 103 184 ?

Options

A. 310
B. 350
C. 305
D. 315

Answer

To solve the number series: 20, 29, 54, 103, 184, ?, we will follow these steps:

### Step 1: Identify the differences between consecutive terms.
- Calculate the difference between each pair of consecutive numbers:
- 29 - 20 = 9
- 54 - 29 = 25
- 103 - 54 = 49
- 184 - 103 = 81

### Step 2: List the differences.
- The differences we found are:
- 9, 25, 49, 81

### Step 3: Recognize the pattern in the differences.
- Notice that these differences are perfect squares:
- 9 = 3²
- 25 = 5²
- 49 = 7²
- 81 = 9²

### Step 4: Identify the next difference.
- The pattern shows that the differences are squares of consecutive odd numbers (3, 5, 7, 9). The next odd number after 9 is 11.
- Therefore, the next difference should be:
- 11² = 121

### Step 5: Add the next difference to the last term in the series.
- Now, add this difference to the last term (184):
- 184 + 121 = 305

### Conclusion
- The number that will come in place of the question mark (?) is **305**.