How is explicit formula for a compound interest geometric sequence?

The explicit formula for compound interest can be expressed as ( A = P(1 + r)^n ), where ( A ) is the amount after ( n ) periods, ( P ) is the principal amount, ( r ) is the interest rate, and ( n ) is the number of compounding periods. This formula represents a geometric sequence because each term (the amount after each compounding period) is derived by multiplying the previous term by a constant factor ( (1 + r) ). Consequently, the sequence of amounts grows exponentially, illustrating the characteristics of geometric growth.