The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,
Sn = (a1(1−r^n) / (1−r)
Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625
Thus, the sum of the first four terms is 26.5625.