The given above is a series that is geometric with the value of common ratio equal to 1/3. The sum of the first six terms of the sequence is,
S6 = a1 x (1 - r^6) / (1 - r)
Substituting the given,
S6 = 6 x (1 - (1/3)^6)/ (1 - 1/3)
The final value of the series is 728/81.
