Correct Answer: 172

Solution : Given:
3, 10, 39, ?, 885, 5346, 37471

Multiply and add the square of the number (starting from 2), to the given numbers, to obtain the next numbers of the given series.
3→(3 × 2) + (2) ² = 6 + 4 = 10
10→(10 × 3) + (3) ² = 30 + 9 = 39
39→(39 × 4) + (4) ² = 156 + 16 = 172
172→(172 × 5) + (5) ² = 860 + 25 = 885
885→(885 × 6) + (6) ² = 5310 + 36 = 5346
5346→(5346 × 7) + (7) ² = 37422 + 49 = 37471

So, 172 is the required number of the given series. Hence, the fourth option is correct.