gebitsreeks

A gebitsreeks is a specific type of mathematical sequence. It is characterized by the fact that the ratio between any term and its preceding term is constant. This constant ratio is known as the common ratio. For example, the sequence 2, 4, 8, 16, 32 is a gebitsreeks where the common ratio is 2. Each term is obtained by multiplying the previous term by 2.

Gebitsreeks can be increasing or decreasing. An increasing gebitsreeks occurs when the absolute value of the common ratio is greater than 1. A decreasing gebitsreeks occurs when the absolute value of the common ratio is between 0 and 1. If the common ratio is 1, all terms in the sequence are the same. If the common ratio is negative, the terms will alternate in sign.

The general formula for the nth term of a gebitsreeks is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number. This formula allows for the calculation of any term in the sequence without having to compute all the preceding terms. Gebitsreeks have applications in various fields, including finance for calculating compound interest, and in physics for describing phenomena like radioactive decay.