, 

Notice that if you leave the numerator as 3 and take half of the denominator,
you get

,

Notice that if you leave the numerator as 3 and take half of the denominator,
you get

, 

Notice that if you leave the numerator as 3 and take half of the denominator,
you get

,

Notice that if you leave the numerator as 3 and take half of the denominator,
you get

,

So you might suspect that to get the next term you might also leave the
numerator as 3 and take half of the denominator.  If you do that you get:

,

And if you got that, you might also suspect that to get the next term
you would also leave the numerator as 3 and take half of the denominator.
If you do that you get: 

 which reduces to 

Leaving the numerator as 3 and taking half of the denominator.
If you do that you get:

  Divide that on your calculator and you get 

Edwin