**Finding the Common Ratio of a Geometric Sequence**In this exercise, we are asked to find the common ratio \( r \) of a geometric sequence. The given information includes:- The first term \( a \) of the sequence is 5.- The 6th term of the sequence is 5120.- It is also given that we should assume \( r > 0 \).To find the common ratio \( r \), we use the formula for the n-th term of a geometric sequence:\[ a_n = a \cdot r^{(n-1)} \]Plugging in the given values:- \( a \) (first term) = 5- \( a_6 \) (6th term) = 5120Thus:\[ 5120 = 5 \cdot r^{5} \]To solve for \( r \), follow these steps:1. Divide both sides of the equation by 5: \[ r^5 = \frac{5120}{5} \] \[ r^5 = 1024 \]2. Take the 5th root of both sides: \[ r = \sqrt[5]{1024} \]3. Calculate the 5th root: \[ r = 4 \]Therefore, the common ratio \( r \) is \( 4 \).**Interactive Example:**- Solve for the common ratio \( r \)- Input box: (for inputting the value of \( r \)).

Name: **Finding the Common Ratio of a Geometric Sequence**In this exercise,
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Finding the Common Ratio of a Geometric Sequence**In this exercise, we are asked to find the common ratio \( r \) of a geometric sequence. The given information includes:- The first term \( a \) of the sequence is 5.- The 6th term of the sequence