Question

Write a sequence that has four geometric means between 31 and –23,540,625.

Answer 1

31, -465, 6975, -104,625, 1,569,375, -23,540,625

Explanation:

Answer 2

`a_n=31(-15)^(n-1)`

31, -465, 6975, -104,625, 1,569,375, -23,540,625

Explanation:

The formula for a geometric sequence is:

`a_n=a_1(r)^(n-1)`

The formula for a geometric sequence is:

Where

r is the common ratio

`a_1` is the first term

`a_n` is the nth term

In this case

`a_1=31`

`a_6=-23,540,625`

So:

`-23,540,625=31(r)^(6-1)`

Now we solve for r

`-23,540,625=31(r)^(5)`

`-(23,540,625)/(31)=r^(5)\\\\r=\sqrt[5]{-(23,540,625)/(31)}\\\\r=-15`

Then the four geometric means are

`a_2=31(-15)^(2-1)=-465`

`a_3=31(-15)^(3-1)=6975`

`a_4=31(-15)^(4-1)=-104,625`

`a_5=31(-15)^(5-1)=1,569,375`

31, -465, 6975, -104,625, 1,569,375, -23,540,625