Select the formula for the n^th term of the sequence. 8,-16,32,ldots 8(-2)^n 8(-2)^n-1 8-2(n) 8-2(n-1) None of the above

To find the formula for the $n^{th}$ term of the sequence $8,-16,32,\ldots$, we need to identify the pattern in the sequence.<br /><br />Let's analyze the given terms:<br />- The first term is $8$.<br />- The second term is $-16$.<br />- The third term is $32$.<br /><br />We can observe that each term is obtained by multiplying the previous term by $-2$. This indicates that the sequence is a geometric sequence with a common ratio of $-2$.<br /><br />The general formula for the $n^{th}$ term of a geometric sequence is given by:<br />$a_n = a_1 \cdot r^{n-1}$<br /><br />Where:<br />- $a_n$ is the $n^{th}$ term<br />- $a_1$ is the first term<br />- $r$ is the common ratio<br />- $n$ is the term number<br /><br />In this case, the first term $a_1$ is $8$ and the common ratio $r$ is $-2$. Substituting these values into the formula, we get:<br />$a_n = 8 \cdot (-2)^{n-1}$<br /><br />Therefore, the correct formula for the $n^{th}$ term of the sequence $8,-16,32,\ldots$ is $8(-2)^{n-1}$.<br /><br />So, the correct answer is: $8(-2)^{n-1}$.