$\text{Which of the following numbers will replace the question mark (?)}\text{in the given series?}$

$5,8,13,?,29,40$

The correct answer is 20.

Step-by-step explanation:

To find the missing number in the series, let's analyze the difference between consecutive terms:

$5,8,13,?,29,40$

First difference:
$8-5=3$

Second difference:
$13-8=5$

Notice that the pattern of differences consists of consecutive odd numbers starting from 3 (i.e., 3, 5, 7, 9, 11...).

Following this pattern, the next difference must be 7. Adding 7 to the third term (13):
$13+7=20$

Let's verify the subsequent terms in the sequence using the next consecutive odd differences (9 and 11):

$20+9=29$

$29+11=40$

Since the pattern holds true for the entire series, the number that replaces the question mark is 20.