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.
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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
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a1 * a2 = 32^2 = 1024
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an = a1 * r^(n-1)
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4 = a1 * r^2
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a2 / a1 = r
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4 = a1 * (a2 / a1)^2
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from first equation
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a1 = 1024 / a2
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now substitute for a1
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4 = (1024/a2) * (a2 / 1024/a2)^2
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4 = (1024/a2) * (a2^2 / 1024) * (a2^2/1024)
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4 = a2 * (a2^2 / 1024)
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a2^3 = 4096
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a2 = 16
a1 = 1024 / 16 = 64
r = 16 / 64 = 1/4
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