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

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Answer 1 · 2017-03-09T21:25:13

$a_n = 6^(2/5 (6 - n))$

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 $r=1/root(6)(36) = 1/6^(2/5)$ and

$c = 36/r = 36 cdot 6^(2/5)$

and the sequence is

$a_n = 6^(2/5 (6 - n))$

How do you find the geometric means in the sequence 32, __, __, __, __, 132, __, __, __, __, 1?