Arithmetic vs geometric sequences
Arithmetic sequences add the same difference each time. Geometric sequences multiply by the same ratio each time. This difference changes how terms grow and how sums are calculated.
The Fibonacci sequence in nature
Fibonacci numbers appear in branching patterns, spiral arrangements, and growth models. The ratio of consecutive terms approaches the golden ratio as the sequence gets larger.
Series vs sequence
A sequence is an ordered list of numbers. A series is the sum of sequence terms. Some geometric series converge to a finite total, while arithmetic and many geometric series diverge as more terms are added.