solve the common ratio in the qeometric sequence 4_,_,_,64​

To find the common ratio of the geometric sequence \(4, \_, \_, \_, 64\), you can use the following steps:1. **Identify the terms**: You know the first term \(a_1 = 4\) and the last term \(a_5 = 64\).2. **Use the formula for the \(n\)-th term of a geometric sequence**: The \(n\)-th term of a geometric sequence can be found using the formula:   \[   a_n = a_1 \cdot r^{(n-1)}   \]   where \(a_n\) is the \(n\)-th term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.3. **Substitute the known values into the formula for the last term**:   \[   64 = 4 \cdot r^{(5-1)}   \]   \[   64 = 4 \cdot r^4   \]4. **Solve for \(r\)**:   \[   64 = 4 \cdot r^4   \]   \[   64 / 4 = r^4   \]   \[   16 = r^4   \]   \[   r = \sqrt[4]{16}   \]   \[   r = 2   \]So, the common ratio \(r\) is \(2\).

Answered by jumongverano | 2024-09-03