SOLUTION: The geometric mean between the first two terms in a geometric sequence is 32. If the third term is 4, find the first term.

Question 1039234: The geometric mean between the first two terms in a geometric sequence is 32. If the third term is 4, find the first term.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
square root(a1 * a2) = 32
:
a1 * a2 = 32^2 = 1024
:
an = a1 * r^(n-1)
:
4 = a1 * r^2
:
a2 / a1 = r
:
4 = a1 * (a2 / a1)^2
:
from first equation
:
a1 = 1024 / a2
:
now substitute for a1
:
4 = (1024/a2) * (a2 / 1024/a2)^2
:
4 = (1024/a2) * (a2^2 / 1024) * (a2^2/1024)
:
4 = a2 * (a2^2 / 1024)
:
a2^3 = 4096
:
*******************
a2 = 16
a1 = 1024 / 16 = 64
r = 16 / 64 = 1/4
*******************
:

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