When you think about compound interest, sequences and series become really important. Let’s break down how they are connected:

1. Understanding Growth: Compound interest increases over time. This growth can be shown using a geometric sequence. Each term in this sequence shows how much money you have at the end of each period.

2. Formula: There’s a simple formula we use:

   $A = P(1 + r/n)^{nt}$

   Here’s what the letters mean:

   • A = the total money you will have after a certain number of years, including interest.
   • P = the initial amount of money you invest.
   • r = the annual interest rate (written as a decimal).
   • n = how often the interest is added (compounding) each year.
   • t = the number of years you keep your money invested.

3. Accumulation: Over time, the series adds up all these growing amounts. This shows us how investments can really grow.

In simple terms, sequences and series help us understand and calculate how our money can increase over time with compound interest!