What is Arithmetic and Geometric Growth?
Arithmetic growth occurs when a constant value is added to a variable at regular intervals, while geometric growth occurs when a variable is multiplied by a constant at regular intervals. In arithmetic growth, the difference between consecutive terms is constant, whereas in geometric growth, the ratio between consecutive terms is constant.
Arithmetic Growth
Equation: $$an = a1 + (n-1)d$$
where:
- $$a_n$$ is the nth term
- $$a_1$$ is the first term
- (d) is the common difference
Geometric Growth
Equation: $$an = a1 * r^(n-1)$$
where:
- (a_n) is the nth term
- (a_1) is the first term
- (r) is the common ratio
Applications
Arithmetic growth is found in situations where the rate of change is constant, such as population growth or the decay of radioactive elements. Geometric growth is found in situations where the rate of change is proportional to the current value, such as compound interest or the spread of infectious diseases.
Related Questions
- What is the difference between arithmetic and geometric growth?
- Arithmetic growth has a constant difference, while geometric growth has a constant ratio.
- How do you calculate the nth term of an arithmetic sequence?
- Use the formula: (an = a1 + (n-1)d).
- How do you calculate the nth term of a geometric sequence?
- Use the formula: (an = a1 * r^(n-1)).
- What is an application of arithmetic growth?
- Population growth.
- What is an application of geometric growth?
- Compound interest.
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