To find the value of S6, we will use the formula for the sum of the first n terms of an arithmetic sequence:

S_n = n/2(2a + (n-1)d)

where:
S_n = sum of the first n terms
n = number of terms
a = first term
d = common difference

Given that B1 = 81 and q = 1/3, we can determine the first term and the common difference for the geometric sequence:

B1 = a
q = d

a = 81
d = 1/3

Now we need to find S6:

S6 = 6/2(2(81) + (6-1)(1/3))
S6 = 3(162 + 5/3)
S6 = 3(486/3 + 5/3)
S6 = 3(491/3)
S6 = 1473/3
S6 = 491

Therefore, S6 is equal to 491.