Answer:
255
Explanation:
The recursive formula is used to find the terms one-by-one, unless you convert it to an explicit formula.
first term (given): 3
2nd term = 4·3 +3 = 15
3rd term = 4·15 +3 = 63
4th term = 4·63 +3 = 255
_____
Looking at the sequence of terms, we see that an explicit formula might be ...
an = 4^n -1
Then the 4th term is
a4 = 4^4 -1 = 256 -1 = 255
_____
Comment on the problem statement
This is NOT an Arithmetic Progression. An arithmetic progression has a common difference between terms. Here, the differences are 12, 48, 192, numbers that are different from one pair of adjacent terms to the next.