In mathematics, sequences and series have various real-life applications that demonstrate their relevance and usefulness. Here are a few examples:

1. Compound Interest: Sequences and series play a vital role in understanding the concept of compound interest. When money is invested or borrowed with compound interest, the amount grows or accumulates according to a geometric sequence. The formula A = P(1 + r)^n can be used to calculate the future value of an investment or loan, where A represents the final amount, P is the principal amount, r is the interest rate per period, and n is the number of periods.

2. Population Growth: Geometric sequences can also be applied to the study of population growth. Let's say the population of a city grows at a constant rate of 5% each year. By representing the initial population as the first term of a geometric sequence and using the nth term formula, we can determine the population size after a certain number of years.

3. Fibonacci Sequence: The Fibonacci sequence, a famous sequence where each term is the sum of the two preceding terms, appears in various natural phenomena such as the breeding patterns of rabbits, branching patterns of trees, and even the Golden Ratio. Understanding the properties of sequences can help us appreciate and comprehend these patterns better.