If b is positive, what is the value of b in the geometric sequence 16, a, 8, b?

Geometric sequences have a common ratio, r    (it's a multiplier)

 

We have:  16,  16r,  16r² = 8,  16r³ 

 

Since  16r² = 8,  r²  =  ½   and  r  =  sqrt(2)/2

 

b  =  8· sqrt(2)/2  =  4·sqrt(2)