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Find the value of r in the following case.The numbers x, y and z are the first three...
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The numbers x, y and z are the first three terms if a geometric sequence with common ratio r, and they are also the first, second and fourth terms of an arithmetic sequence.
Now the terms of a GP are written as a*r^(n-1)
So x = a*r^0
y = a*r
z = a*r^2
Now they are also the 1st , 2nd and 4th terms of an AP. So the difference between the 4th and the 2nd terms is twice that between the 2nd and 1st terms.
So 2*(y - x) = ( z - y)
=> 2(ar - a) = ( ar^2 - ar)
=> 2a ( r - 1) = ar(r - 1)
=> 2 = r
=> r = 2
Therefore the common ratio is 2.
Posted by justaguide on December 4, 2010 at 4:21 AM (Answer #1)
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