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## #1 2006-10-22 10:04:16

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### finding the nth term

does anyone know how to write out the nth term? here is my problem...

1   2    3   4     5      6    n     20
.............................................

2   -1   -4   -7  -10  -13   ?     ?

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## #2 2006-10-22 11:04:02

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

Subtracting 3 each time.

And we know that when n=1, then the answer is 2, so:

f(n) = 5-3n

Last edited by MathsIsFun (2006-10-22 11:07:34)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #3 2006-10-22 11:06:34

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

wait so did you get 4 becasue 4-3=1? and how would you take that formula and find the 20th term?

Last edited by mathgeek62 (2006-10-22 11:10:09)

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## #4 2006-10-22 11:08:32

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

Ha ... you caught me as I was editing my answer.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #5 2006-10-22 11:11:23

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

f(20) = 5 - 3×20 = 5-60 = -55

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #6 2006-10-22 11:13:18

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

wait so how did you get 5-3n?

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## #7 2006-10-22 11:19:13

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

Once I knew that it was "-3" each time, the next thing I wanted to know was what it is when n=0

I knew it was 2 when n=1, so I went "backwards", or "+3" to get my 5

So now I know that f(0) = 5

And that for every extra "n" it is "-3", so I get the whole formula: f(n) = 5-3n

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #8 2006-10-22 11:21:02

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

And here is the graph: Plot of 5-3n

You can see why I wanted f(0)=5, that gives me my starting point

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #9 2006-10-22 11:25:02

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

ok that makes sense but why do you need to find 0?? is that for every problem you do??

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## #10 2006-10-22 11:28:54

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

1     2     3     4     5    6
....................................

1    4     9     16    25    36

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## #11 2006-10-22 11:49:01

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

well isn't it increasing by 1 every time?

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## #12 2006-10-22 11:51:46

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

Well, you don't have to go for f(0), but it does make it easier.

Now the next problem is simply squaring: 1[sup]2[/sup]=1, 2[sup]2[/sup]=4, etc

so f(n) = n[sup]2[/sup]

And yes, the "difference" does increase each time (by 2), which says something interesting about squaring.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #13 2006-10-22 11:53:14

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: finding the nth term

Have you ever heard of a square root?

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #14 2006-10-22 11:59:24

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

ok so you just say n2 when you are squaring? and im still not sure about the first problem because i dont get how you got f(n)=5??

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## #15 2006-10-22 12:02:31

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

The "2" has to be written smaller and higher, but yes. Or you could simply say f(n) = n×n

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #16 2006-10-22 12:06:50

MathsIsFun
Registered: 2005-01-21
Posts: 7,663

### Re: finding the nth term

You know how the first problem was "-3" each time?

So what happens when you go backwards (5,4,3,2,1)? The answer increases by 3 each time, right? Example: from 2 to 1 then answer goes from -4 to -1.

So to go from 1 to 0 means you have to add 3 to the answer. The answer for 1 was "2", so the answer for 0 must be "2+3" equals 5.

The handy thing about 0 is that you can forget about the "3n", because 3×0=0.

so f(0)=5 only works for 0 [that is why I wrote f(0), not f(n)]

For all other values you need f(n) = 5-3n

Try it out:

f(1) = 5-3 = 2
f(2) = 5 - 3×2 = 4-6 = -1
etc

Oh, and the formula does work for 0 of course: f(0) = 5 - 3×0 = 5-0 = 5

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #17 2006-10-22 12:07:44

mathgeek62
Member
Registered: 2006-10-22
Posts: 8

### Re: finding the nth term

ohhhhhh ok so let me try a problem

1       2      3       4        5
.............................................

6     12       18      24      30

so would it be 6n-12 ???

Last edited by mathgeek62 (2006-10-22 12:23:04)

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## #18 2006-10-22 21:42:36

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: finding the nth term

Close but no. The numbers go up by 6 each time, so there is a 6n in there, as you rightly put. However, if we go back from 1 to get f(0), then that is 6-6=0, so we don't need to add or take anything away.