Answer:
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. When plotted on a graph, an arithmetic sequence forms a straight line. This linear graph reflects the constant rate of change between terms.
A geometric sequence, on the other hand, is a sequence where each term is found by multiplying the previous term by a constant factor. The graph of a geometric sequence, when plotted, shows an exponential growth or decay pattern, depending on whether the common ratio is greater than or less than 1. The exponential nature of the graph is characterized by its curved shape, indicating rapid growth or decay.
Comparing them to functions:
- **Arithmetic Sequence vs. Linear Function:**
- Both exhibit a constant rate of change.
- The arithmetic sequence forms a discrete set of points along a straight line, while the linear function is continuous.
- **Geometric Sequence vs. Exponential Function:**
- Both involve a constant ratio between terms.
- The geometric sequence represents discrete points on a curve, while the exponential function is continuous and smoothly curves.
In summary, arithmetic sequences and linear functions share a linear relationship, while geometric sequences and exponential functions exhibit exponential growth or decay patterns.