Changes in Sequences 🔄📈

Geometric Sequence Identification

Checking if the ratio between successive terms is constant to determine if a sequence is geometric

Discrete Graph

A graph consisting of distinct, separate points, not connected by lines or curves

Geometric Sequence

A sequence where successive terms have a constant ratio, behaving like exponential functions but not continuous

Common Ratio

The constant factor by which successive terms are multiplied in a sequence that behaves exponentially

Arithmetic Sequence

A sequence where successive terms have a constant difference, behaving like linear functions but not continuous

Nth Term Formula for Geometric Sequence

g_n=g_k×r^n-k, where g_k​ is a known term, r is the constant ratio, and n is the term number

Exponential Function Characteristic

A function where the rate of change is proportional to the current value, represented graphically by a curved line

Sequence Graphing Rule

Points are plotted but cannot be connected, representing a non-continuous function

Common Difference

The constant rate of change between successive terms in a sequence that behaves linearly

Linear Function Characteristic

A function with a constant rate of change, represented graphically by a straight line

Sequence

A function from whole numbers to real numbers, where only whole numbers can be input but any real number can be output

Nth Term Formula for Arithmetic Sequence

a_n=a_k+d(n-k), where a_k is a known term, d term is the constant difference, and n is the term number

Arithmetic Sequence Identification

Checking if the difference between successive terms is constant to determine if a sequence is arithmetic