For this sequence compute...

Jul 2008
212
2
For the sequence compute a6^2 (note the six is below the 2 - I hope you know what I mean) - i'm assuming it's just a6 to the power of 2.

a0 = 1
an+1 = (an +(3/an))/2

I've already found all the terms from a0 to a6 if that will help.
 
Nov 2009
927
260
Wellington
Since you tell us you know \(\displaystyle a_6\), isn't it sort of trivial to compute \(\displaystyle a_6 ^2\) ? Can you explain in more detail please ?
 
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pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
Yep \(\displaystyle a_6^2\) , now what did you get for \(\displaystyle a_6\) ?
 
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Jul 2008
212
2
Hi Bacterius and pickslides,

Well, for a6 I did [a5 + (3/a5)]/2 = [1.732051 +(3/1.732051)]/2 which equals 1.732051 (to 6dp) so do I just do 1.732051^2?

Sorry if this is a dumb question. (blush)
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
Hi Bacterius and pickslides,

Well, for a6 I did [a5 + (3/a5)]/2 = [1.732051 +(3/1.732051)]/2 which equals 1.732051 so do I just do 1.732051^2?

Sorry if this is a dumb question. (blush)
That's what I would do. (Nod)
 
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Nov 2009
927
260
Wellington
Well \(\displaystyle a_6 ^2\) is the same as \(\displaystyle (a_6)^2\), so you basically just have to square the sixth term, yes.

But it seems too simple somehow. Are you sure the question didn't refer to \(\displaystyle a_{6^2}\) ? (this is equivalent to \(\displaystyle a_{36}\))
 
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Jul 2008
212
2
Haha okay thanks the answer is 3, thanks a lot.
 
Jul 2008
212
2
Well \(\displaystyle a_6 ^2\) is the same as \(\displaystyle (a_6)^2\), so you basically just have to square the sixth term, yes.

But it seems too simple somehow. Are you sure the question didn't refer to \(\displaystyle a_{6^2}\) ? (this is equivalent to \(\displaystyle a_{36}\))
Hey Bacterius,
Yes the question is just the power one (it's only one part of the question as a whole, so that's not the only thing asked!)
Thanks for your help!
 
Nov 2009
927
260
Wellington
Indeed :)

EDIT : yep, I just saw that \(\displaystyle a_6\) was the square root of 3, which made it clear that the question asked \(\displaystyle a_6 ^2\). Thanks for replying though.