Find out the missing term of the number series given below.

15, 34, 57, 86, ?, 154

The correct option is 117.

To find the missing term in the given number series, let us analyze the differences between consecutive terms:
First term = 15
Second term = 34
Third term = 57
Fourth term = 86
Fifth term = ?
Sixth term = 154

Let us calculate the differences between consecutive terms:
Difference between the second and first term:
$34-15=19$
Difference between the third and second term:
$57-34=23$
Difference between the fourth and third term:
$86-57=29$

Observe the sequence of differences: 19, 23, and 29. These differences are consecutive prime numbers.
Following this pattern, the next difference should be the next prime number after 29, which is 31.
Therefore, the fifth term is calculated as:
$86+31=117$

To verify this pattern, the next prime number after 31 is 37.
Adding 37 to the fifth term (117) should give the sixth term:
$117+37=154$
Since this matches the final term in the series (154), the pattern is correct, and the missing term is indeed 117.