9 15 24 ? 51 69 90

Options

A. 27
B. 30
C. 36
D. 38

Explanation

To find the missing number in the series: 9, 15, 24, ?, 51, 69, 90, we will analyze the differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the series**:
The given series is: 9, 15, 24, ?, 51, 69, 90.

2. **Calculate the differences between consecutive terms**:
- Difference between 15 and 9:
\[ 15 - 9 = 6 \]
- Difference between 24 and 15:
\[ 24 - 15 = 9 \]
- Difference between 51 and 24 (we will calculate this later).
- Difference between 69 and 51:
\[ 69 - 51 = 18 \]
- Difference between 90 and 69:
\[ 90 - 69 = 21 \]

3. **List the differences**:
We have the following differences so far:
- From 9 to 15: 6
- From 15 to 24: 9
- From 24 to ?: ?
- From ? to 51: ?
- From 51 to 69: 18
- From 69 to 90: 21

4. **Analyze the pattern in the differences**:
The differences we have are: 6, 9, ?, 18, 21.
Let's see if we can find a pattern:
- The difference between 6 and 9 is 3.
- The difference between 9 and the next difference (which we need to find) should also follow a pattern.

5. **Continuing the pattern**:
If we assume the differences are increasing by 3:
- After 6, we have 9 (which is 6 + 3).
- The next difference should be 12 (which is 9 + 3).
- Then we have 18 (which is 12 + 6).
- Finally, 21 (which is 18 + 3).

6. **Fill in the missing difference**:
The missing difference between 24 and the next number should be 12.

7. **Calculate the missing number**:
To find the missing number, we add the missing difference (12) to 24:
\[ 24 + 12 = 36 \]

8. **Conclusion**:
The missing number in the series is **36**.

### Final Answer:
The missing number is **36**.

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