Arithmetic Progression
Discrete Sequence Generator
Explore discrete functions
Sequences & Series Patterns
Discover the discrete nature of sequences. See how arithmetic progressions form lines, geometric ones grow exponentially, and alternating series exhibit distinct oscillatory behavior across the coordinate plane.
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Key Concepts
Arithmetic Sequence
A sequence where each term increases or decreases by a constant difference, forming a linear pattern of discrete points.
Geometric Sequence
A sequence where each term is multiplied by a constant ratio, forming an exponential curve.
Alternating Sequence
A sequence whose terms alternate between positive and negative values, often caused by a negative common ratio.
Discrete Functions & Envelopes
A sequence is essentially a function whose domain is restricted to positive integers (1, 2, 3...). As a result, sequences manifest graphically not as a smooth continuous curve, but rather as an ordered set of discrete points.
An arithmetic sequence acts exactly like a linear function (y = mx + c), while a geometric sequence follows an exponential function curve (y = a*r^x).
By visualizing these sequences on a grid, you can immediately see their long-term behavior: whether they diverge to infinity, decay to zero, or oscillate across the horizontal axis.