Which number will replace (?) in the following series?
4, 5, 8, 10, 12, 15, 16, 20, ?, 25, .......

Options

A. 24
B. 21
C. 20
D. 22

Answer

To find the missing number in the series: 4, 5, 8, 10, 12, 15, 16, 20, ?, 25, we can analyze the pattern in the series.

### Step 1: Identify the differences between consecutive terms.
- 5 - 4 = 1
- 8 - 5 = 3
- 10 - 8 = 2
- 12 - 10 = 2
- 15 - 12 = 3
- 16 - 15 = 1
- 20 - 16 = 4
- ? - 20 = ?
- 25 - ? = ?

### Step 2: Write down the differences.
The differences between the numbers are:
1, 3, 2, 2, 3, 1, 4, ?, ?

### Step 3: Look for a pattern in the differences.
The differences appear to alternate somewhat:
- 1, 3, 2, 2, 3, 1, 4

We can observe that the differences do not follow a strict pattern, but we can see that:
- After 20, if we assume the next difference is 4 (continuing the pattern of increasing differences), we can find the missing number.

### Step 4: Calculate the missing number.
If we take the last number in the series before the question mark (20) and add 4:
- 20 + 4 = 24

### Step 5: Verify the next term.
Now, check if adding the next difference (1) gives us the next term:
- 24 + 1 = 25

This confirms that our assumption is correct.

### Conclusion:
The number that will replace (?) in the series is **24**.