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The terms \(140, a, \frac{45}{28}\) are the first, second and third terms, respectively, of a geometric sequence. If \(a\)  is positive, what is the value of  \(a\) ?

ant101  Jan 15, 2018
 #1
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Sqrt[ (45/28) / 140] =3/28 - Common ratio.

3/28 x 140 = 15 - the 2nd term "a"

Guest Jan 15, 2018
 #2
avatar+86890 
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140, a,  45/28

 

Let r be the common ratio...so

 

140r  = a      ⇒  r  =  a /140

 

So..this implies that

 

a (a / 140)   =  45/28

 

a^2  =  (140*45) / 28

 

a^2   = 5 * 45

 

a^2  =  225   

 

a =  15

 

 

cool cool cool

CPhill  Jan 15, 2018

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