For this sequence compute...

brumby_3

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.

Bacterius

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 ?

brumby_3

pickslides

MHF Helper
Yep $$\displaystyle a_6^2$$ , now what did you get for $$\displaystyle a_6$$ ?

brumby_3

brumby_3

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
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)

brumby_3

Bacterius

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 $$\displaystyle a_{36}$$)

brumby_3

brumby_3

Haha okay thanks the answer is 3, thanks a lot.

brumby_3

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!)
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.