What is a sequence? It is a set of

What is a sequence? It is a set of numbers which are written in some particular order. For example,take the numbers
1 , 3 , 5 , 7 , 9 , …

Here, we seem to have a rule. We have a sequence of odd numbers. To put this another way, we start with the numbers 1, which is an odd number, and then each successive number is obtained by adding 2 to give the next odd number.
Here is another sequence :
1 , 4 , 9 , 16 , 25 , …

This is the sequence of square numbers. And this sequence,
1 , -1 , 1 , -1 , 1 , -1 , …

Is a sequence of numbers alternating between 1 and -1. In each case, the dots written at the end indicate that we must consider the sequence as an infinite sequence, so that it goes on for ever
On the other hand, we can also have finite sequence.
The numbers
1, 3, 5, 9

Form a finite sequence containing just four numbers.
The numbers
1, 4, 9, 16

Also form a finite sequence. And so do these,
the numbers
1, 2, 3, 4, 5, 6, …, n.

These are the numbers we use for counting, and we have included n of them. Here, the dots indicate that we have not written all the numbers down explicitly. The n after the dots tells us that this is a finite sequence, and that the last number is n.

Here is a sequence that you might recognise :
1 , 1 , 2 , 3 , 5 , 8 , …

This is an infinite sequence where each term (form the third term onwards) is obtained by adding together the two previous terms.This is called the Fibonacci sequence.
We often use an algebraic notation for sequence. We might call the first term in a sequence