Find the indicated term for the geometric sequence.
$\frac{-5}{243}, \frac{5}{81}, \frac{-5}{27}, \ldots ;$ the 8 th term
Answer
\(\boxed{45}\) is the 8th term of the geometric sequence.
Step 1 ：Identify the first term (\(a_1\)) of the geometric sequence, which is \(-\frac{5}{243}\) or approximately -0.0205761316872428.
Step 2 ：Find the common ratio (\(r\)) by dividing any term by the previous term. In this case, \(r = -3.0\).
Step 3 ：Identify the term number (\(n\)) that we want to find, which is 8.
Step 4 ：Use the formula for the nth term of a geometric sequence, \(a_n = a_1 * r^{(n-1)}\), where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.
Step 5 ：Substitute the values into the formula: \(a_8 = -\frac{5}{243} * (-3)^{8-1}\).
Step 6 ：Simplify the expression to get the 8th term of the geometric sequence, which is 45.
Step 7 ：\(\boxed{45}\) is the 8th term of the geometric sequence.
