Math Help - sequences- covergent?

1. sequences- covergent?

${a_{n + 1}} = \sqrt {2{a_n}}
$

Is this a convergent sequence and if so, what does it converge to?

I have no idea how to beginning this...

2. Originally Posted by genlovesmusic09
${a_{n + 1}} = \sqrt {2{a_n}}
$

Is this a convergent sequence and if so, what does it converge to?

I have no idea how to beginning this...
What is the first term?

Graphing some terms for $a_n = 1$ it looks like it converges to 2.

3. I wasn't given a first term which is why I am having I problem

but ${a_n} = 1$?

4. It is easy to see that the series converges for any value of $a_1>0$
if $a_1=0$ then the series converges to zero.

Now lets assume that $a_n>2$ then it follows that:

$a_{n+1}=\sqrt{2a_n}<\sqrt{a_n\cdot a_n}=a_n$

And

$a_{n+1}=\sqrt{2a_n}>\sqrt{2\cdot2}=2$

So you see that if $a_n>2$ then: $2.

Now what happens if $a_n<2$ ??

Hope that helps.