Exercise 33 Page 712

We want to find the geometric means in the given sequence. To do so, we first have to find the value of the common ratio r. 8, , , , 648 From the sequence, we know the value of the first term and that there are 5 total terms. We can substitute 8 for a_1 and 5 for n in the general formula for the nth term of a geometric sequence. a_n=a_1r^(n-1) ⇒ a_5= 8r^(5-1) We also know that the value of the fifth term is 648. We can substitute this in the above formula and solve for r.

We found that r is either 3 or - 3. We will use this to calculate the three geometric means. Let's start with r=3.

Finally, let's calculate the geometric means when r=- 3.