Glossary
Arithmetic sequence
A sequence where the difference between any two consecutive terms is constant.
Example:
If your savings account balance increases by 100, 200, ...), that's an arithmetic sequence.
Common difference (d)
The constant value added or subtracted to each term to get the next term in an arithmetic sequence.
Example:
In the sequence 7, 10, 13, 16, ..., the common difference is 3.
Common ratio (r)
The constant value by which each term is multiplied to get the next term in a geometric sequence.
Example:
In the sequence 5, 15, 45, 135, ..., the common ratio is 3.
Constant Proportional Change (Geometric)
Describes how terms in a geometric sequence change by a fixed multiplicative factor, equivalent to the common ratio, leading to exponential growth or decay.
Example:
The value of an investment growing by 5% each year demonstrates a constant proportional change.
Constant Rate of Change (Arithmetic)
Describes how terms in an arithmetic sequence increase or decrease by the same fixed amount, equivalent to the common difference, resulting in linear growth.
Example:
A car traveling at a steady 60 miles per hour exhibits a constant rate of change in distance over time.
Discrete points
Individual, separate points on a graph that represent the terms of a sequence, as the inputs are whole numbers rather than a continuous range.
Example:
When plotting the population of a town each year, you'd see discrete points for each year, not a continuous line, because population is measured annually.
Geometric sequence
A sequence where the ratio between any two consecutive terms is constant.
Example:
If a bacterial colony doubles its size every hour (100, 200, 400, 800, ...), that's a geometric sequence.
Sequence
An ordered list of numbers, essentially a function that maps whole numbers (positions) to real numbers (terms).
Example:
The number of push-ups you do each day for a week (10, 12, 15, 18, 20, 22, 25) forms a sequence.