Find the \( 14^{\text {th }} \) term of the following geometric sequence. \[ 1,3,9,27, \ldots \]

To find the \( 14^{\text{th}} \) term of the geometric sequence given by \( 1, 3, 9, 27, \ldots \), we first identify the first term and the common ratio of the sequence. The first term \( a \) is: \[ a = 1 \] Next, we find the common ratio \( r \) by dividing the second term by the first term: \[ r = \frac{3}{1} = 3 \] The general formula for the \( n^{\text{th}} \) term of a geometric sequence is given by: \[ a_n = a \cdot r^{n-1} \] To find the \( 14^{\text{th}} \) term, we set \( n = 14 \): \[ a_{14} = 1 \cdot 3^{14-1} = 1 \cdot 3^{13} \] Now, we need to calculate \( 3^{13} \). We can compute this step by step: \[ 3^1 = 3 \] \[ 3^2 = 3 \cdot 3 = 9 \] \[ 3^3 = 3 \cdot 9 = 27 \] \[ 3^4 = 3 \cdot 27 = 81 \] \[ 3^5 = 3 \cdot 81 = 243 \] \[ 3^6 = 3 \cdot 243 = 729 \] \[ 3^7 = 3 \cdot 729 = 2187 \] \[ 3^8 = 3 \cdot 2187 = 6561 \] \[ 3^9 = 3 \cdot 6561 = 19683 \] \[ 3^{10} = 3 \cdot 19683 = 59049 \] \[ 3^{11} = 3 \cdot 59049 = 177147 \] \[ 3^{12} = 3 \cdot 177147 = 531441 \] \[ 3^{13} = 3 \cdot 531441 = 1594323 \] Thus, the \( 14^{\text{th}} \) term of the sequence is: \[ \boxed{1594323} \]