To determine the 10th term of the geometric sequence given by the formula [tex]\( a(n) = -3 \cdot 2^{n-1} \)[/tex], let's follow the steps to find the value:
1. Identify the formula: [tex]\( a(n) = -3 \cdot 2^{n-1} \)[/tex].
2. Plug in [tex]\( n = 10 \)[/tex] into the formula:
[tex]\[
a(10) = -3 \cdot 2^{10-1}
\][/tex]
3. Simplify the exponent:
[tex]\[
a(10) = -3 \cdot 2^9
\][/tex]
4. Evaluate [tex]\( 2^9 \)[/tex]. Here, [tex]\( 2^9 \)[/tex] equals 512:
[tex]\[
a(10) = -3 \cdot 512
\][/tex]
5. Multiply -3 by 512:
[tex]\[
-3 \cdot 512 = -1536
\][/tex]
Thus, the 10th term of the geometric sequence [tex]\( a(n) = -3 \cdot 2^{n-1} \)[/tex] is [tex]\( -1536 \)[/tex].
So, the correct answer is:
[tex]\[
-1536
\][/tex]
