Question

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

Answer 1

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

Explanation:

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}`