87 ? 144 204 285 387
Find the missing number in the following number series.

The correct answer is 105 (Option 105).

To find the missing number in the given number series, let us analyze the differences between consecutive terms:

Given series:
87, ?, 144, 204, 285, 387

First, let us calculate the difference between the known consecutive terms towards the end of the series:

$387-285=102$

$285-204=81$

$204-144=60$

Now, let us examine the differences obtained so far: 60, 81, 102.
Notice the pattern in these differences (the second difference):

$102-81=21$

$81-60=21$

Since the second difference is constant (+21), we can work backwards to find the preceding differences:

The difference between 144 and the missing number (?) should be:
$60-21=39$

Therefore, the missing number (?) is:
$144-39=105$

To verify, let us check the difference between 105 and the first term (87):
$39-21=18$
$87+18=105$

The pattern holds true consistently throughout the series. Thus, the missing number is 105.