The given recurrence relation starts with and increases by 0.5 for each subsequent value of . So, if we calculate a few terms, we find , , , and so on. This pattern reveals that can be expressed explicitly as , showcasing a linear relationship that makes it easy to predict future values!

In real-world situations, this type of sequence can model scenarios where an initial value increases at a consistent rate over time. For instance, if you’re tracking the growth of a plant that grows half an inch each week, starting from 3 inches, you would use a similar mathematical approach to predict its height over the weeks!