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

1 Answer
Oct 19, 2016

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}