The nth term of a sequence is \(2^{2n-1}\). Which term of the sequence is \(2^9?\)
Question 1 Report
The nth term of a sequence is \(2^{2n-1}\). Which term of the sequence is \(2^9?\)
Answer Details
To find which term of the sequence is \(2^9\), we need to solve for n in the equation \(2^{2n-1}=2^9\).
First, we can simplify the equation by dividing both sides by \(2^9\), giving us \(2^{2n-1-9}=2^{2n-10}=1\).
Next, we can solve for n by taking the logarithm of both sides of the equation. Since any logarithm base can be used, we can use the natural logarithm, denoted as ln:
\begin{align*}
2n-10 &= \ln 1 \\
2n-10 &= 0 \\
2n &= 10 \\
n &= 5
\end{align*}
Therefore, the fifth term of the sequence is \(2^9\).
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