Question

The first term of a geometric sequence is 32, and the 5th term of the sequence is 818 .

What are the geometric means between these terms?


Enter your answer by filling in the boxes to correctly complete the geometric sequence. Enter any fractions as simplified fractions.

Answer 1

Explanation:

Answer 2

`32,24,18,(27)/(2) ,(81)/(8)`

Explanation:

Let x, y , and z be the numbers.

Then the geometric sequence is
`32,x,y,z,(81)/(8)`

Recall that term of a geometric sequence are generally in the form:

`a,ar,ar^2,ar^3,ar^4`

This implies that:

a=32 and
`ar^4=(81)/(8)`

Substitute a=32 and solve for r.

`32r^3=(81)/(8)`

`r^4=(81)/(256)`

Take the fourth root to get:

`r=\sqrt[4]{(81)/(256) }`

`r=(3)/(4)`

Therefore
`x=32*(3)/(4) =24`

`y=24*(3)/(4) =18`

`z=18*(3)/(4) =(27)/(2)`