To calculate the sum of the first six terms of a geometric series, you can use the formula for the sum of the first \( n \) terms:
\[ S_n = a \frac{1 - r^n}{1 - r} \]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( a \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the number of terms.
In this case:
- \( a = 2 \),
- \( r = 3 \),
- \( n = 6 \).
Now plug in the values:
\[ S_6 = 2 \frac{1 - 3^6}{1 - 3} \]
Calculating \( 3^6 \):
\[ 3^6 = 729 \]
Now substitute this back in:
\[ S_6 = 2 \frac{1 - 729}{1 - 3} = 2 \frac{1 - 729}{-2} = 2 \frac{-728}{-2} \]
Simplifying:
\[ S_6 = 2 \cdot 364 = 728 \]
So, the sum of the first six terms of the geometric series is 728.