Find the missing term – 3, 4, 12, ___, 196, 1005

To find the missing term in the sequence 3, 4, 12, __, 196, 1005, let's analyze the pattern between consecutive numbers:

Pattern Analysis
3 to 4: 3 * 1 + 1 = 4

4 to 12: 4 * 2 + 4 = 12

12 to ?: 12 * 3 + 9 = 36 + 9 = 45

45 to 196: 45 * 4 + 16 = 180 + 16 = 196

196 to 1005: 196 * 5 + 25 = 980 + 25 = 1005

The pattern involves multiplying the current term by an increasing integer (1, 2, 3, 4, 5) and adding the square of that same integer (1^2, 2^2, 3^2, 4^2, 5^2).

Following this logic, the missing term is 45.