Find the sum \( S_{7} \) of the first 7 terms of the geometric sequence with \( a_{1}=2 \) and \( r=3 \). Use the formula \( S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r} \). \[ S_{7}=\square \] Question Help: \( \square \) Video Submit Question

To find the sum \( S_{7} \) of the first 7 terms of the geometric sequence with \( a_{1}=2 \) and \( r=3 \), we can use the formula \( S_{n}=\frac{a_{1}(1-r^{n})}{1-r} \). Substituting the given values \( a_{1} = 2 \), \( r = 3 \), and \( n = 7 \): \[ S_{7} = \frac{2(1-3^{7})}{1-3} \] Calculating \( 3^{7} \): \[ 3^{7} = 2187 \] Now, substituting this back into the sum formula: \[ S_{7} = \frac{2(1-2187)}{1-3} = \frac{2 \times -2186}{-2} = 2186 \] So, we have: \[ S_{7} = 2186 \]