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

The correct option is 105.

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

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

Let us calculate the differences between the known adjacent terms:

204 - 144 = 60

285 - 204 = 81

387 - 285 = 102

Now, let us examine the pattern in these differences (the second difference):

81 - 60 = 21

102 - 81 = 21

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

The difference prior to 60 should be:

60 - 21 = 39

The difference prior to 39 should be:

39 - 21 = 18

Now, let us apply these differences to find the missing term (?):

First term = 87

Second term (?) = 87 + 18 = 105

Let us verify with the next term:

Third term = 105 + 39 = 144

This matches the given term 144 perfectly.

Therefore, the missing number in the series is 105.