9, 11, 17, 29, 49, ?
Find the missing number in the following number series.

The correct answer is 79.

To find the missing number in the given series, we need to analyze the pattern of differences between consecutive terms. Let's list the terms of the series and find the difference between each term and the next:
Let the terms be:
$a_1=9$
$a_2=11$
$a_3=17$
$a_4=29$
$a_5=49$
$a_6=?$

Now, let's calculate the first-level differences:
First difference: $11-9=2$
Second difference: $17-11=6$
Third difference: $29-17=12$
Fourth difference: $49-29=20$

The sequence of differences is: 2, 6, 12, 20.
Let's analyze the pattern in this sequence of differences by finding the differences of these differences (second-level differences):
Difference between 6 and 2: $6-2=4$
Difference between 12 and 6: $12-6=6$
Difference between 20 and 12: $20-12=8$

The second-level differences are: 4, 6, 8.
This is an arithmetic progression increasing by 2 each time (4, 6, 8, ...).
Following this pattern, the next second-level difference should be:
$8+2=10$

Now, we add this value to the last first-level difference (20) to find the next difference in the sequence:
Next first-level difference = $20+10=30$

Finally, we add this difference to the last term of the series (49) to find the missing number:
Missing number = $49+30=79$