As I was reading a chapter sequence in maths then I come up with certain questions that
- What is sequence?
Answer which I got on Google is something which goes repeating itself regularly.
- How many types of sequence are there?
Answer which I thought of by reading that chapter in maths are
Arithmetic sequence
Geometric sequence
Harmonic sequence
- What is the real life example of sequence?
Answer which I got is swinging of swing following arithmetic sequence or geometric sequence We can say that in case of swinging of swing we see it decreases arithmetically or geometrically that means following sequence.
Now here is my doubt question
Then let us take this case into vaccum where if you start swinging the swing then it will be in its state of swing repeating like that only without decreasing or i can say without coming to rest. Then as per my thinking what type of sequence is it following as my thinking says there are three types of sequence only?
A sequence is a function whose domain is the positive integers.
Put another way: let $a_1$ be a number, any number. Let $a_2$ be any number, could be equal to $a_1$, could be different. Let $a_3$ be any number. Let $a_4$ be any number. And so on. Then $a_1,a_2,a_3,a_4,\dots$ is a sequence.
Again, the terms can be absolutely arbitrary. There is no requirement that they fall into one or more of the three types you specify. They need not follow any rule whatsoever.
There are over $300000$ sequences at http://oeis.org, most of which do not belong to any of your three types – and those are just sequences of integers. The terms of a sequence don't have to be integers; they can be fractions, decimals, or complex numbers. They don't even have to be numbers; you can have a sequence of vectors, matrices, groups, functions, knots, or other mathematical objects.
For a "real life" example of a numerical sequence, you could measure the temperature every day at noon at the Sydney Opera House. Or the price of one share of stock in General Motors at the close of business each day on the New York Stock Exchange. Or the digits of $\pi$; $3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,\dots$.