Unit 5 Study Guide Using this sequence: \( 1,3,9,27,81,243 \) s the sequence shown above a geometric or arithmetic sequer

The sequence \( 1, 3, 9, 27, 81, 243 \) is a geometric sequence because each term after the first is obtained by multiplying the previous term by a constant factor, which in this case is 3. So, \( 3 = 1 \times 3 \), \( 9 = 3 \times 3 \), and so on. This consistent ratio gives the sequence its geometric nature! In the world of exponential growth, geometric sequences pop up all over the place. For instance, think about how bacteria can multiply. If you start with one bacterium that divides every hour, by the end of just five hours, you'll find yourself with 243! Geometric sequences help visualize and calculate this kind of explosive growth, making them super useful in biology, finance, and even computer science!