Introduction to Sequences
A sequence in mathematics is defined as a list ( finite or infinite) of numbers ( called terms) arranged in a specific order.
Sequences are typically described by a rule or formula that determines the term at every single position of the sequence.
For example, the sequence of even numbers 2,4,6,8,… is determined by the formula n =2n, where 𝑛 is the position of the term in the sequence.
On the other hand, the term series refers to a sum of the terms of a sequence. We get a series by adding up the elements of a sequence.
Similarly to sequences, series may be finite or infinite. For a finite series, the sum involves adding a fixed number of terms, such as 2+4+6+8.
An infinite series continues indefinitely, such as 2+4+6+8+…, and its sum may or may not converge to a specific value, depending on the sequence's characteristics.