Sequences & Series

A sequence is a set of numbers in a particular order. A series is the sum of the consecutive terms in a sequence. Sequences and series can be written in mathematical notation using summation symbols.

Some types of sequences are arithmetic, where each term is separated from the previous term by a constant difference. For example, the sequence 5, 10, 15, 20 is an arithmetic sequence with common difference 5. Geometric sequences have a common ratio between terms. For example, the sequence 2, 6, 18, 54 is a geometric sequence with common ratio 3.

Fibonacci numbers form a sequence where each term is the sum of the previous two terms. This sequence appears in nature in the spirals of shells and in the arrangement of leaves on a stem.

The study of sequences and series can help us to find patterns and to make predictions. It is also useful in solving mathematical problems.