Fill the missing number for the series from the given options:
8, 11, 16, 23, 32,?
(a)40
(b)43
(c)46
(d)42

Options

A. 40
B. 43
C. 46
D. 42

Answer

To find the missing number in the series 8, 11, 16, 23, 32, ?, we will analyze the differences between consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Write down the series**:
The series given is:
\[ 8, 11, 16, 23, 32, ? \]

2. **Calculate the differences between consecutive terms**:
- Difference between 11 and 8:
\[ 11 - 8 = 3 \]
- Difference between 16 and 11:
\[ 16 - 11 = 5 \]
- Difference between 23 and 16:
\[ 23 - 16 = 7 \]
- Difference between 32 and 23:
\[ 32 - 23 = 9 \]

So, the differences are:
\[ 3, 5, 7, 9 \]

3. **Identify the pattern in the differences**:
The differences themselves form a sequence:
\[ 3, 5, 7, 9 \]
We can see that the differences are increasing by 2 each time.

4. **Find the next difference**:
Following the pattern, the next difference after 9 would be:
\[ 9 + 2 = 11 \]

5. **Add the next difference to the last term of the series**:
Now, we add this difference to the last term in the series (32):
\[ 32 + 11 = 43 \]

6. **Conclusion**:
Therefore, the missing number in the series is:
\[ \boxed{43} \]