Find the $n$th term $a_{n}$ of the geometric sequence described below, where $r$ is the common ratio.
\[
a_{6}=-1024, r=-4
\]
\[
a_{n}=\square
\]
Answer
So, the nth term of the sequence is given by: \(\boxed{a_n = (-4)^{(n-1)}}\)
Step 1 ：Given that the 6th term of the geometric sequence is -1024 and the common ratio is -4, we can use the formula for the nth term of a geometric sequence to find the first term. The formula is \(a_n = a_1 * r^{(n-1)}\)
Step 2 ：Substitute the given values into the formula: \(-1024 = a_1 * (-4)^{5}\)
Step 3 ：Solve for \(a_1\): \(a_1 = -1024 / -1024 = 1\)
Step 4 ：Now that we have \(a_1\), we can substitute it into the formula to find \(a_n\): \(a_n = 1 * (-4)^{(n-1)}\)
Step 5 ：So, the nth term of the sequence is given by: \(\boxed{a_n = (-4)^{(n-1)}}\)
