Answer:
[tex]a_n=31(-15)^{n-1}[/tex]
31, -465, 6975, -104,625, 1,569,375, -23,540,625
Step-by-step explanation:
The formula for a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]
The formula for a geometric sequence is:
Where
r is the common ratio
[tex]a_1[/tex] is the first term
[tex]a_n[/tex] is the nth term
In this case
[tex]a_1=31[/tex]
[tex]a_6=-23,540,625[/tex]
So:
[tex]-23,540,625=31(r)^{6-1}[/tex]
Now we solve for r
[tex]-23,540,625=31(r)^{5}[/tex]
[tex]-\frac{23,540,625}{31}=r^{5}\\\\r=\sqrt[5]{-\frac{23,540,625}{31}}\\\\r=-15[/tex]
Then the four geometric means are
[tex]a_2=31(-15)^{2-1}=-465[/tex]
[tex]a_3=31(-15)^{3-1}=6975[/tex]
[tex]a_4=31(-15)^{4-1}=-104,625[/tex]
[tex]a_5=31(-15)^{5-1}=1,569,375[/tex]
31, -465, 6975, -104,625, 1,569,375, -23,540,625
Answer:
31, -465, 6975, -104,625, 1,569,375, -23,540,625
Step-by-step explanation:
