If five geometric means are inserted between 8 and 5832, what is the fifth term in the geometric series?
Again i don't understand the wording of the problem.
So in general: what does it mean for $n$ means to be inserted between $a$ and $b$, and in particular when those means are geometric?
On
Take the $6$th root of $\frac{5832}{8}$, which turns out to be $3$.
So, the sequence is $8$,$24$,$72$,$216$,$648$,$1944$,$5832$
A series is geometric, if $\frac{a_{k+1}}{a_k}=q$ for all $k\ge 1$.
In other words, to get the next member of the sequence, you must multiply the actual one with some constant number $q$.
I think its means that $$8,a_2,a_3,a_4,a_5,a_6,5832$$ is a geometric series. Find $a_5$.
Then, $$8\cdot x^6=5832.$$ Then $x^6=729$ and $x=3$.
Therefore, $$a_5=8\cdot 3^4=648.$$