To find the sum of the first \( n \) terms of a geometric series, we can use the formula:
\[ S_n = a \frac{1 - r^n}{1 - r} \]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( a \) is the first term,
- \( r \) is the common ratio, and
- \( n \) is the number of terms.
In this case, the first term \( a \) is 3, the common ratio \( r \) is 2, and the number of terms \( n \) is 8.
Substituting these values into the formula gives us:
\[ S_8 = 3 \frac{1 - 2^8}{1 - 2} \]
First, calculate \( 2^8 \):
\[ 2^8 = 256 \]
Now substitute back into the formula:
\[ S_8 = 3 \frac{1 - 256}{1 - 2} \]
This simplifies to:
\[ S_8 = 3 \frac{1 - 256}{-1} = 3 \frac{-255}{-1} = 3 \times 255 = 765 \]
Thus, the sum of the first eight terms of the geometric series is:
\[ \boxed{765} \]
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