How do you find the geometric means in the sequence #4, , , __, 324#?

Question

16504 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-19T10:50:15

Middle terms are #{12,36,108}# or #{-12,36,-108}#

It appears that questioner wants to know three middle terms in the geometric sequence #{4,... ,... ,... ,324}#

Let the first term be #a# and common ratio be #r#.

Then five terms are #{a,ar,ar^2,ar^3,ar^4}#

Hence #a=4# and #ar^4=324#, Dividing latter by former, we get

#r^4=324/4=81# and hence #r=+-3#

Hence geometric sequence is #{4,12,36,108,324}# or #{4,-12,36,-108,324}#

and middle terms are #{12,36,108}# or #{-12,36,-108}#

How do you find the geometric means in the sequence #4, __, __, __, 324#?