37, 39, 81, 247, ?, 4971
Find the missing number in the following number series.

The correct option is 993.

To find the missing number in the series, let us analyze the pattern of progression between consecutive terms.

The pattern follows a rule where the next term is obtained by multiplying the current term by an increasing integer (starting from 1) and then adding the next consecutive integer (starting from 2):

First transition:

$37\times 1+2=39$

Second transition:

$39\times 2+3=81$

Third transition:

$81\times 3+4=247$

Fourth transition (to find the missing number):

$247\times 4+5=988+5=993$

Fifth transition (to verify the final term):

$993\times 5+6=4965+6=4971$

Thus, the calculations confirm that the missing number in the series is 993.