What is the general term formula of the following number series?
1, √2/2, 1/2, √2/4, 1/4.

Question

What is the general term formula of the following number series?
1, √2/2, 1/2, √2/4, 1/4.

xapproachesinfinity · Answer

First what is the first term and the ratio
how did we get from 1 to $\large \frac{\sqrt{2}}{2}$

anonymous · Answer

Maybe 1*√2/2?

anonymous · Answer

@xapproachesinfinity

xapproachesinfinity · Answer

there is no may be here my friend. there is only it is or not hehe
so to go from 1 to root2/2 you need to multiply by 1/root2
and then again from root2/2 you multiply by 1/root2 you 1/2 and so on
therefore we call that number we are multiplying by the ratio of a geometric sequence
the first term is 1 since we started with that number!

xapproachesinfinity · Answer

By now since you are taking this course you should be familiar with the general form of this sequence

anonymous · Answer

So， 1*√2/2=√2/2

  √2/2*√2/2=2/4=1/2

   1/2* √2/2=√2/4
   
  √2/4*√2/2=2/8=1/4.

anonymous · Answer

Am I right?

xapproachesinfinity · Answer

Correct! that number root2/2 is the ratio

xapproachesinfinity · Answer

denoted r for geometric sequences

anonymous · Answer

And the general term formula is
$$\left( √2/2\right)^{n-1}$$

xapproachesinfinity · Answer

Correct!

anonymous · Answer

Thank you!

xapproachesinfinity · Answer

just don't forget the first term in other examples
in this case is 1 so i doesn't affect the form

xapproachesinfinity · Answer

You are wlm!