1.2 In a geometric sequence in which all terms are \( p \) the \( 3^{\text{rd}} \) term (term number three) is \( \frac{1}{3} \) and the 11 Determine the constant ratio.

In a geometric sequence, each term can be expressed as \( a_n = a_1 \cdot r^{n-1} \) where \( r \) is the constant ratio. Given the third term \( a_3 = \frac{1}{3} \), we can write this as \( a_1 \cdot r^2 = \frac{1}{3} \). If we denote the first term as \( a_1 = p \), we have \( p \cdot r^2 = \frac{1}{3} \). To find the constant ratio \( r \), we would also need another term from the sequence or a relationship between terms, such as \( a_{11} \). If \( a_{11} = p \cdot r^{10} \), you can create a system of equations. Without a specific value for \( a_{11} \), we can only express the constant ratio in terms of \( p \): 1. From \( p \cdot r^2 = \frac{1}{3} \), isolate \( p \): \( p = \frac{1}{3r^2} \). 2. Substitute \( p \) in \( a_{11} = p \cdot r^{10} \). Now you can solve for \( r \) once you have the value for \( a_{11} \) to determine the specific constant ratio! Would you like to explore further with a specific value?