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As I was reading a chapter sequence in maths then I come up with certain questions that

  1. What is sequence?

Answer which I got on Google is something which goes repeating itself regularly.

  1. 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

    1. 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?

mathematics2x2life
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user87284
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2 Answers2

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What is sequence?

Answer which I got on Google is something which goes repeating itself regularly.

I don't know where or how you got that answer, but it is wrong. The first hit on google, if I google "sequence", is this wikipedia article which, correctly, defines a sequence as

an enumerated collection of objects in which repetitions are allowed and order does matter.

There is no need for anything to repeat. There exist plenty of sequences where nothing in them repeats. For example, the sequence $1,2,3,4,5,\dots$ does not repeat itself.

How many types of sequence are there?

What do you mean by "type" of 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.

I have no idea what you mean by that. In what way does a swing "follow an arithmetic sequence"?

5xum
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  • ....if I take your example 1,2,3,4...and so on here you can see they are increasing arithmetically by 1 – user87284 Mar 09 '20 at 09:27
  • Or i can say 1 is repeating itself – user87284 Mar 09 '20 at 09:27
  • In case of swinging of swing you can notice if you take that swing to certain feet suppose 4 feet high then when it will come again to that same position its feet would decrease let suppose 3 then 2 then 1 again following arithmetic sequence – user87284 Mar 09 '20 at 09:30
  • By the way the Wikipedia article you linked is the same that OP referred to as chapter – Maximilian Janisch Mar 09 '20 at 09:33
  • @user87284 Ok, sure, $1$ is "repeating itself". But that's a pretty wide definition of "repeating". So please, define exactly what you mean by "repeating", and I can explain to you whether by that definition, a sequence "repeats itself regularly". – 5xum Mar 09 '20 at 09:41
  • My question is that everything which goes on repeating is a sequence – user87284 Mar 09 '20 at 09:46
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    @user87284 I don't understand your question. What's more, what you wrote is not a question, it is a statement. What's more, what you wrote down is a false (or, at least, inaccurate) statement. Please, rephrase what you are saying so that we can understand each other. – 5xum Mar 09 '20 at 09:50
  • If something is in order as well as repeating itself then ...can we call that sequence – user87284 Mar 11 '20 at 08:44
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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 $\pi$; $3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,\dots$.

Gerry Myerson
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