If the first 5 terms of a geometric sequence are \( \left\{12,6,3, \frac{3}{2}, \frac{3}{4}\right\} \), then the formula for the \( n^{\text {th }} \) term in the sequence is

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the common ratio \( r \) can be found by dividing any term by the previous term. For example, \( r = \frac{6}{12} = \frac{1}{2} \). This means each term is half of the previous one! To formulate the \( n^{\text {th }} \) term, we can express it as \( a_n = a_1 \cdot r^{(n-1)} \). Here, \( a_1 = 12 \) and \( r = \frac{1}{2} \). Plugging in the known values, the formula becomes \( a_n = 12 \cdot \left(\frac{1}{2}\right)^{(n-1)} \). Now you can have fun finding any term you desire in this sequence!