Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then the 4th term is:

Let 'a' and 'd' be the first term and common difference respectively.
Sum of the first 9 terms = 9[2a + 8d]/2 = 9(a + 4d)
Given that 200 < 9(a + 4d) < 220
a + d = 12
a + 3d = x
200/9 < a + 4d < 220/9
22.22 < a + 4d < 24.44
Since a + d = 12, a = 12 - d
Substitute this into the inequality:
22.22 < 12 - d + 4d < 24.44
22.22 < 12 + 3d < 24.44
10.22 < 3d < 12.44
3.40 < d < 4.14
Since 'd' must be an integer, d can be 4.
Then a = 12 - 4 = 8
The 4th term is a + 3d = 8 + 3(4) = 8 + 12 = 20