Question 72205: Find the missing geometric sequence 15, __ , 81,...
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Find the missing geometric sequence 36, __ , 100, ...
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Found 2 solutions by pradhyumna.kumar@gmail.com, stanbon:
Answer by pradhyumna.kumar@gmail.com(62)   (Show Source):
You can put this solution on YOUR website! Find the missing geometric sequence 15, __ , 81,...
the missing term is (t2/t1)=(t3/t2)
=> (t2/15)=(81/t2)
=> (t2)^2 = 81 * 15
=> t2 = 9 sqrt(15).
Find the missing geometric sequence 36, __ , 100, ...
the missing term is (t2/t1)=(t3/t2)
=> (t2/36)=(100/t2)
=> (t2)^2 = 100 * 36
=> t2 = 10 * 6 = 60 .
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find the missing geometric sequence 15, __ , 81,...
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If it's a geometric sequence there must be a "common ratio" "r" between
the terms.
So the terms are 15, 15r,(15r)r
Thus 15r^2=81
r^2=81/15
r=9/sqrt15
So the missing element is 15(9/sqrt15) = 9sqrt15
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Find the missing geometric sequence 36, __ , 100, ...
Following the same argument as above:
36r^2=100
r^2=100/36
r=10/6 = 5/3
Therefore the missing term is 36(5/3)=60
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Cheers,
Stan H.
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