Find the missing terms in each geometric sequence.

a. 3,___, ___, ___, 768

768 = 3r^5-1   divide both sides by 3

256  = r⁴     take the 4th root of each side

4  = r

So ....terms 2 - 4 are given by : 

a₂  = 3(4)^2-1  = 3(4)¹ =   12

a₃  = 3(4)^3-1 = 3(4)²  = 48

a₄  = 3(4)^4-1= 3(4)³ = 192      

b. ___,___,144,___,___,___,9

9  =     a₁(r)⁶     (1)

144  = a₁(r)²     (2)

Divide (1) by (2)   and we have

9/144  = r⁴    →    1/16  = r⁴    take the 4th root of both sides  →  r = 1/2

So ....   using (1)

9 = a₁ (1/2)⁶

9 = a₁ (1/64)    multiply both sides by 64

576  = a₁     and each successive term is 1/2 of the previous one.....

So......term 2  =  576/2  = 288

And terms  4 - 6  are     72, 36, 18