In the study of how diseases spread, sequences are really helpful. Let’s break it down step by step:

1. Starting Point: When a disease first appears, only a few people usually get sick. We can think of this first group as the beginning of a sequence, let's call it $a_1$.

2. How It Grows: Each person who gets sick can pass the disease to others. If we assume each sick person infects a certain number of people, we can make a sequence to show how the cases might increase over time.

   For example, if each person spreads the disease to 2 more people, our sequence would look like this:

   • $a_1 = 1$ (the first person)
   • $a_2 = 2$ (people infected by the first)
   • $a_3 = 4$ (people infected by the second)

   So, the pattern continues like this: $a_n = 2^{n-1}$ for the $n$th term.

3. Making Predictions: Using these sequences helps us guess how many people might get sick after a while. This information is important for keeping public health in check. If we know how many cases to expect, we can make sure there are enough resources, like vaccines, available.

4. Controlling the Spread: We can also create sequences for different situations, like when people keep their distance from one another or when a vaccine is ready. This helps us understand how to manage a pandemic better.

So, sequences aren’t just about numbers; they are like a map that helps us understand and deal with disease outbreaks!