# How do you find the geometric means in the sequence 32, __, __, __, __, 1?

Mar 9, 2017

${a}_{n} = {6}^{\frac{2}{5} \left(6 - n\right)}$

#### Explanation:

If $36$ is a term of a geometric sequence, then

$36 = c \cdot r$

but we know also

$1 = c \cdot {r}^{6}$

dividing term to term we obtain

$36 = {r}^{-} 6$ so $r = \frac{1}{\sqrt[6]{36}} = \frac{1}{6} ^ \left(\frac{2}{5}\right)$ and

$c = \frac{36}{r} = 36 \cdot {6}^{\frac{2}{5}}$

and the sequence is

${a}_{n} = {6}^{\frac{2}{5} \left(6 - n\right)}$