Question 1052696: If x, y and z are consecutive terms in a geometric sequence, then y over z is equal to z over y. Show that the following numbers are consecutively in a geometric sequence:
A) 5, square root of 35 and 7
B) a, square root of ab and b
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If x, y and z are consecutive terms in a geometric sequence, then y over z is equal to z over y. Show that the following numbers are consecutively in a geometric sequence:
A) 5, square root of 35 and 7
r = sqrt(35)/5
r = 7/sqrt(35) = 7*sqrt(35)/35 = sqrt(35)/5
Since the ratios are the same, the sequence is geometric.
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B) a, square root of ab and b
r = sqrt(ab)/a
r = b/sqrt(ab) = b*sqrt(ab)/ab = sqrt(ab)/a
Since the ratios are the same, the sequence is geometric.
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Cheers,
Stan H.
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