Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary. \[ 4, \quad 12, \quad 36, \ldots \] Sum of a finite geometric series: \[ S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r} \]

To find the sum of the first 10 terms of the sequence \( 4, 12, 36, \ldots \), we need to identify the first term \( a_1 \) and the common ratio \( r \). Here, \( a_1 = 4 \) and the common ratio can be calculated as \( r = \frac{12}{4} = 3 \). Using the sum formula for a finite geometric series \( S_n = \frac{a_1(1 - r^n)}{1 - r} \), we can substitute in our values: \[ S_{10} = \frac{4(1 - 3^{10})}{1 - 3} = \frac{4(1 - 59049)}{-2} = \frac{4(-59048)}{-2} = \frac{236192}{2} = 118096 \] Thus, the sum of the first 10 terms of the sequence is \( 118096 \).