Find the \( 11^{\text {th }} \) term of the following geometric sequence. \[ 4,8,16,32, \ldots \]

To find the 11th term of a geometric sequence, we need to know the first term and the common ratio. Given geometric sequence: \(4, 8, 16, 32, \ldots\) The first term (\(a\)) is 4, and the common ratio (\(r\)) can be found by dividing any term by the previous term. Let's find the common ratio: \(r = \frac{8}{4} = 2\) Now, we can use the formula for the nth term of a geometric sequence: \(a_n = a \cdot r^{n-1}\) where: - \(a_n\) is the nth term - \(a\) is the first term - \(r\) is the common ratio - \(n\) is the term number Substitute the values we have: - \(a = 4\) - \(r = 2\) - \(n = 11\) \(a_{11} = 4 \cdot 2^{11-1}\) Now, we can calculate the 11th term. Calculate the value by following steps: - step0: Calculate: \(4\times 2^{11-1}\) - step1: Subtract the numbers: \(4\times 2^{10}\) - step2: Rewrite the expression: \(2^{2}\times 2^{10}\) - step3: Calculate: \(2^{12}\) - step4: Evaluate the power: \(4096\)