Series Convergence

[Windway]

Hello!

I need to determine whether the sequence below converges or diverges.
a₁=1;
a_n+1=4-a_n
for n>=1

I don't have a clue as to how I could solve this.
Any input would be appreciated.
Thank you.

 

[yoscar04]

You should show us what have you tried so far.
Maybe start by writing down a few terms of the sequence.

 

[pka]

[QUOTE="Windway, post: 507680, member: 83583"
I need to determine whether the sequence below converges or diverges.
a₁=1;
a_n+1=4-a_n
for n>=1[/QUOTE]
Is it sequence or a series? The thread title says series but the post says sequence. Which is it?

 

[pka]

In my reply #3, I want you to see the difference in sequence and series.
Often students confuse the two terms.
Sequences are functions from the natural numbers to a number field.
A Series is a sum of a sequence..
A sequence converges if it has a unique limit point (a condensation point). Almost all of the terms are "close to" a unique point.
A Series converges if the sequence if its partial sums converges: \(\mathop {\lim }\limits_{N \to \infty } \left( {\sum\limits_{n = 1}^N {{a_n}} } \right) = S\) Note that the series diverges if its sequence diverges.
That said: look at this link. Can you see neither sequence nor series can converge?

 

[Dr.Peterson]

I need to determine whether the sequence below converges or diverges.
a₁=1;
a_n+1=4-a_n
for n>=1

I don't have a clue as to how I could solve this.
Any input would be appreciated.

@yoscar04's advice in post #2 is excellent; you may not realize how good it is:

You should show us what have you tried so far.
Maybe start by writing down a few terms of the sequence.

Please do what he said and just write out a few terms, and you should see very quickly how to proceed. Then write back, so we know whether you need more help.

It is also good general advice: When you don't know what to do with a problem, sit down and do something. If you can do nothing else, just play with it and get a feel for how it works.