Sequences and Series


A sequence is a list of numbers, usually made according to some pattern, such as

1, 2, 3, 4, ........

which is the list of counting numbers. A sequence can have a fixed number of terms. Such sequence is known as finite. The sequence can also be infinite, or having indefinitely many terms.

Series

A series is the sum of terms in a sequence. For example,

2 + 3+ 4 + 5 + 6.

in this set the series is adding up the terms of the finite sequence, 2, 3, 4, 5, 6.

Also a series can be finite or infinite, but at this time we will only work with finite series. In the previous series, let's add up the numbers, the  answer is  known as the sum of the series. In our example, 20 is the sum of the above series.

Sometimes a sequence can be ascending ( numbers increasing from beginning to end). The other way around, a sequence is descending, if the numbers are decreasing from the beginning to the end of the sequence.

Examples:

State whether the sequences are ascending or descending sequences:

1) 2, 4, 7, 9, 11, 14 ...

Solution

This particular sequence is ascending as the numbers get larger as the sequences progresses.

2) 13, 10, 7, 5, 3 ...

Solution

This sequence is descending, as the numbers get smaller as the sequence progresses.

In learning sequences and series, there are two other types of sequences that one must learn and understand:

1) Arithmetic Sequence

2) Geometric Sequence

3) Finding Sums of Series