Question

Find 5 geometric mean between 1 and 27?

Answer 1

Five geometric mean between `1` and `27` are `sqrt3,3,3sqrt3,9,9sqrt3`

Explanation:

Let the five geometric mean between `1` and `27` be `a,b,c,d` and `e`. In other words

`1,a,b,c,d,e,27` are in geometric sequence, with first term as `1` and assume common ration is `r`. Then as `27` is seventh term, we have

`1*r^6=27` i.e. `r^6=27=3^3=(sqrt3)^6`

and hence `r=sqrt3`

and five geometric mean between `1` and `27` are

`sqrt3,3,3sqrt3,9,9sqrt3`