# How to give inductive definition to sequence?

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Give inductive definition for the following:

1). 120, 60, 30, 15, 7.5, …

2). 4, 9, 19, 39, 79, …

1). 120, 60, 30, 15, 7.5, …

2). 4, 9, 19, 39, 79, …

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#2

(Original post by

Give inductive definition for the following:

1). 120, 60, 30, 15, 7.5, …

2). 4, 9, 19, 39, 79, …

**TSRforum**)Give inductive definition for the following:

1). 120, 60, 30, 15, 7.5, …

2). 4, 9, 19, 39, 79, …

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(Original post by

What two things do you need to define a sequence inductively?

**SeanFM**)What two things do you need to define a sequence inductively?

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#4

(Original post by

No idea. I can only define arithmetic sequences using a and d.

**TSRforum**)No idea. I can only define arithmetic sequences using a and d.

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Does that help?

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(Original post by

That's kind of like an inductive definition for a sequence, in that the first term, = a, and you're given that and

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Does that help?

**SeanFM**)That's kind of like an inductive definition for a sequence, in that the first term, = a, and you're given that and

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Does that help?

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#6

(Original post by

I don't think you can use that for the sequences I posted.

**TSRforum**)I don't think you can use that for the sequences I posted.

The answers aren't going to look exactly like that but something similar.

What is the first term in sequence 1? And what is the relationship between two consecutive terms?

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(Original post by

Then the question would be impossible to solve

The answers aren't going to look exactly like that but something similar.

What is the first term in sequence 1? And what is the relationship between two consecutive terms?

**SeanFM**)Then the question would be impossible to solve

The answers aren't going to look exactly like that but something similar.

What is the first term in sequence 1? And what is the relationship between two consecutive terms?

There is no extra information, that's all that's given.

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#8

(Original post by

That's where the sequence starts and the relationship isn't stated.

There is no extra information, that's all that's given.

**TSRforum**)That's where the sequence starts and the relationship isn't stated.

There is no extra information, that's all that's given.

That is where the sequence starts, yes, so the first term must be there at the start.

The relationship isn't stated but you should be able to identify it.

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(Original post by

You are reading my questions in the wrong way

That is where the sequence starts, yes, so the first term must be there at the start.

The relationship isn't stated but you should be able to identify it.

**SeanFM**)You are reading my questions in the wrong way

That is where the sequence starts, yes, so the first term must be there at the start.

The relationship isn't stated but you should be able to identify it.

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#10

(Original post by

I know the relationship, but now how would I turn it into an inductive definition? Also here's another sequence: 1, 3, 11, 43, 171, … relationship is a bit harder to find there but I still can't turn it into a I.Definition.

**TSRforum**)I know the relationship, but now how would I turn it into an inductive definition? Also here's another sequence: 1, 3, 11, 43, 171, … relationship is a bit harder to find there but I still can't turn it into a I.Definition.

If we had an arithmetic series 5, 15, 25, .... then you would tell me that a = 5 and d = 10. I'm hesitant to use this as an example as we are not to confuse the formula for the nth term, n = a + (n--1)d for an inductive definition because it is not. An inductive definition uses other terms to work out the n+1 th term.

So for that example, we can safely say that 5 is the first term in the sequence so and the relationship between two terms is that you add 10 each time, so the definition is that

, so when n = 2 you use a1 to find that a2 = 15, use a2 to find a3 which is 25... and so on, which is the magic of induction.

So in Q1, I'll tell you that a1 = 120. What's the relationship between that and a2, and how can we express it like above?

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#11

**TSRforum**)

That's where the sequence starts and the relationship isn't stated.

There is no extra information, that's all that's given.

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(Original post by

Sean isn't asking for extra information - you should be able to answer the questions by looking at the given values and *thinking*. Explicity: try to think what operation(s) you might use to get from 120 to 60, and from 60 to 30, and so on.

**DFranklin**)Sean isn't asking for extra information - you should be able to answer the questions by looking at the given values and *thinking*. Explicity: try to think what operation(s) you might use to get from 120 to 60, and from 60 to 30, and so on.

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#13

(Original post by

I know how to find the relationship but then how do I turn it into a inductive definition?

**TSRforum**)I know how to find the relationship but then how do I turn it into a inductive definition?

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(Original post by

OK, explain what the relationship is.

**DFranklin**)OK, explain what the relationship is.

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#15

(Original post by

x1/2 to get next term

**TSRforum**)x1/2 to get next term

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(Original post by

So what is an algebraic relationship connecting a given term with the next term in the sequence,

**16Characters....**)So what is an algebraic relationship connecting a given term with the next term in the sequence,

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#17

(Original post by

1/2Un?

**TSRforum**)1/2Un?

Then this, together with your first term is your inductive definition:

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(Original post by

Yes,

Then this, together with your first term is your inductive definition:

**16Characters....**)Yes,

Then this, together with your first term is your inductive definition:

Or can you have indices or brackets aswell?

e.g. Un+1 = (Un -3)^2 -3/4

If not then I just need to find out what I can times Un by then what I need to add or subtract after that to get the next term?

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#19

(Original post by

Is this how it will always be written: Un+1 = Un + c or Un+1 = Un

Or can you have indices or brackets aswell?

e.g. Un+1 = (Un -3)^2 -3/4

If not then I just need to find out what I can times Un by then what I need to add or subtract after that to get the next term?

**TSRforum**)Is this how it will always be written: Un+1 = Un + c or Un+1 = Un

Or can you have indices or brackets aswell?

e.g. Un+1 = (Un -3)^2 -3/4

If not then I just need to find out what I can times Un by then what I need to add or subtract after that to get the next term?

What it will actually involve in your exam depends on your specification. If it is for A Level I do not imagine the recurrence relationship (the relationship between two consecutive terms) will be too complicated.

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(Original post by

The relationship between successive terms could be anything, it could involve adding, multiplying or indices.

What it will actually involve in your exam depends on your specification. If it is for A Level I do not imagine the recurrence relationship (the relationship between two consecutive terms) will be too complicated.

**16Characters....**)The relationship between successive terms could be anything, it could involve adding, multiplying or indices.

What it will actually involve in your exam depends on your specification. If it is for A Level I do not imagine the recurrence relationship (the relationship between two consecutive terms) will be too complicated.

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