To find the 8th term of the geometric sequence, we need to use the given formula of the sequence:
[tex]\[
a_n = 3 \cdot 2^{(n-1)}
\][/tex]
Here, [tex]\( a_1 = 3 \)[/tex], which is the first term, and [tex]\( r = 2 \)[/tex], which is the common ratio. We want to find the 8th term ([tex]\( a_8 \)[/tex]), so we substitute [tex]\( n = 8 \)[/tex] into the formula:
[tex]\[
a_8 = 3 \cdot 2^{(8-1)}
\][/tex]
Simplifying the exponent:
[tex]\[
a_8 = 3 \cdot 2^7
\][/tex]
Next, we calculate [tex]\( 2^7 \)[/tex]:
[tex]\[
2^7 = 128
\][/tex]
Now, we multiply this result by 3:
[tex]\[
a_8 = 3 \cdot 128 = 384
\][/tex]
So, the 8th term of the geometric sequence is:
[tex]\[
\boxed{384}
\][/tex]
Hence, the correct answer is B. 384.
