Find the 8th term of the geometric sequence \( 6,18,54, \ldots \) Answer Attempt 1 out of 3

To find the 8th term of the given geometric sequence, we first determine the common ratio. The common ratio \( r \) is calculated by dividing the second term by the first term: \[ r = \frac{18}{6} = 3 \] Now, we can find the nth term of a geometric sequence using the formula: \[ a_n = a_1 \cdot r^{(n-1)} \] where \( a_1 \) is the first term (6), \( r \) is the common ratio (3), and \( n \) is the term number (8 in this case). Plugging in the values: \[ a_8 = 6 \cdot 3^{(8-1)} = 6 \cdot 3^7 \] Calculating \( 3^7 \): \[ 3^7 = 2187 \] Now substituting back: \[ a_8 = 6 \cdot 2187 = 13122 \] Thus, the 8th term of the geometric sequence is **13122**.