SOLUTION: Insert 4 geometric means between 1/8 and 64. I've worked on this so far: an = a₁r^n – 1 a₁ = 1/8, a₆ = 64 64 = (1/8)r⁶⁻' r⁵ = 512 r =

Algebra ->  Sequences-and-series -> SOLUTION: Insert 4 geometric means between 1/8 and 64. I've worked on this so far: an = a₁r^n – 1 a₁ = 1/8, a₆ = 64 64 = (1/8)r⁶⁻' r⁵ = 512 r =       Log On


   

Question 925566: Insert 4 geometric means between 1/8 and 64.
I've worked on this so far:
an = a₁r^n – 1
a₁ = 1/8, a₆ = 64
64 = (1/8)r⁶⁻'
r⁵ = 512
r = 4
an = a₁r^n – 1
an = (1/8)(4)4^n – 1
and I don't know if I'm wrong or not, so please let me know if I am.
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
+an+=+a1%2A+r%5E%28n-1%29
a1 = 1/8
a6=64
+64=+%281%2F8%29+%2A+r+%5E%286-1%29
+64+=%281%2F8%29%2Ar%5E5
move 8 to th right
+64%2A8++=+r%5E5
512+=+r%5E5
here "r" is not equals to 4

r= 3.48
+a2++=%281%2F8%29+%2A+%283.48%29%5E%282-1%29
+a2=0.435
+a3+=+%281%2F8%29%2A+%283.48%29%5E%283-1%29
=%281%2F8%29%2A3.48%5E2
=1.5138
+a4++=+%281%2F8%29%2A+%283.48%29%5E%284-1%29
=+%281%2F8%29%2A+42.14
=5.26
+a5++=++%281%2F8%29%2A+3.48%5E%285-1%29
=18.33
so four geometric means = 0.435 , 1.5138,5.26,18.33
Remarks: As per my observation , r may not be 3.48. I hope there is mistake in the problem. it should be 1/16 instead of 1/8
then r = 4
a2 = 1/4
a3 = 1
a4 = 4
a5 =16