The first term of a geometric sequence is 48, and the 5th term of the sequence is 243/16. What are the geometric means between these terms? 48,_,_,_,243/16 please quick it's urgent

Guest Feb 26, 2022

#1**+1 **

First, I think you are supposed to find out all the 5 terms of the GS between 48 and 243/16

[243/16] / 48 ==0.31640625

0.31640625^(1/4) ==**3 /4 - this is the common ratio.**

The 5 terms of your GS look like this:

**48 , 36 , 27 , 81 / 4 , 243 / 16 , >>Number of terms = 5>>Total Sum == 2343 / 16**

Note: I don't think you need "geometric means"!!

Guest Feb 26, 2022

#2**+1 **

I agree with the answers from guest; however, if you are to use geometric means:

The geometric mean of a and b is sqrt( a · b).

Therefore the geometric mean between 48 and 243/16 is:

sqrt( 48 · 243/16 ) = 27 (the third term, or center term)

Then, the geometric mean between 48 and 27 is:

sqrt( 48 · 27 ) = 36 (the second term)

and the geometric mean between 27 and 243/16 is:

sqrt( 27 · 243/16 ) = 81/4 (the fourth term)

geno3141 Feb 26, 2022