Let the first term of the geometric series be a and the common ratio be r.
The formula for the sum of the first n terms of a geometric series is: S_n = a(r^n - 1)/(r - 1)
Given that the sum of the 3rd to 7th term is 3267, we can write: S_7 - S_2 = 3267 a(r^7 - 1)/(r - 1) - a(r^2 - 1)/(r - 1) = 3267 a(r^7 - r^2) = 3267(r - 1)
Since the common ratio is 3, we can substitute r = 3 into the equation: a(3^7 - 3^2) = 3267(3 - 1) a(2187 - 9) = 6534 a(2178) = 6534 a = 6534/2178 a = 3
Therefore, the first term of the geometric series is 3.