Question Find the 13 th term of the geometric sequence \( 5,10,20, \ldots \) Answer Attempt tout of 3 \( \square \)

To find the 13th term of the geometric sequence \( 5, 10, 20, \ldots \), we first need to identify the first term and the common ratio. 1. **Identify the first term (\( a \))**: - The first term \( a = 5 \). 2. **Identify the common ratio (\( r \))**: - The common ratio can be found by dividing the second term by the first term: \[ r = \frac{10}{5} = 2 \] 3. **Use the formula for the \( n \)-th term of a geometric sequence**: The formula for the \( n \)-th term (\( T_n \)) of a geometric sequence is given by: \[ T_n = a \cdot r^{(n-1)} \] where \( a \) is the first term, \( r \) is the common ratio, and \( n \) is the term number. 4. **Substitute the values to find the 13th term**: - Here, \( n = 13 \): \[ T_{13} = 5 \cdot 2^{(13-1)} = 5 \cdot 2^{12} \] Now, we will calculate \( 2^{12} \) and then multiply by 5. Let's calculate \( 2^{12} \) first. \[ 2^{12} = 4096 \] Now, substituting back into the equation for \( T_{13} \): \[ T_{13} = 5 \cdot 4096 = 20480 \] Thus, the 13th term of the geometric sequence is \( 20480 \).