Find the Nth Term: Expression for a Sequence of Fractions

[cybercrypt13]

Homework Statement

Find an expression for the nth Term:

{ 1/3, 1, 7/5, 5/3, 13/7 }

Homework Equations

The Attempt at a Solution

The problem has obviously had its fractions reduced on almost every case if not every case. I've been working on this problem for at least 4 hours and have had no luck what so ever seeing a solution. Any help would be appreciated.

 

[lalbatros]

You can re-write that as follows:

1/3 , 4/4 , 7/5 , 10/6 , 13/7 , ...

therefore the n-term is: (1+(n-1)*3) / (3+(n-1))

This is not mathematics, but a kind of game.
Was that part of a math homework?

 

[Gib Z]

This is not mathematics, but a kind of game.

Mathematics is one big fun game :)

 

[cybercrypt13]

Yes, my professor is making me want to quit... Instead of testing us on the stuff he's teaching he gives us problems we've never seen before and grades us on it. All problems in the book are all left in their expanded form so you can try to look for a pattern. This guy gives us problems that you have unscrew before you can actually show him you know how to work things.

Thanks a bunch for the help...

 

[cybercrypt13]

And honestly, I don't know that I'd have even figured out the nth term as fast as you did if at all... We've worked a total of 2 problems using this stuff before we moved on to other stuff. You obviously have this subject mastered... :-)

 

[lalbatros]

Well,

I guessed the result,
but you should think if there is no systematic way to find it out.

Of course this would need some assumption, otherwise there are an infinite number of solutions to such a problem.

For example, you might assume the general term is of the following form:

tn = (a n + b)/(c n +d)

this would lead you to a linear system with three unknowns: b/a, c/a, d/a.
You should then check if it is compatible with the 5 data you have been given.

Maybe this is what your teacher expects from you?

 

[group1element]

Can someone help solve this?
Find the nth term and the sum of the first nth term of the series: 2+22+222+2222+_ _ _ _ __+.

Kindly help with it.

 

[SammyS]

Hijacked Thread

Can someone help solve this?
Find the nth term and the sum of the first nth term of the series: 2+22+222+2222+_ _ _ _ __+.

Kindly help with it.

Please start your own thread.

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 Do not hijack an existing thread with off-topic comments or questions--start a new thread.