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+2
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avatar+803 

Let \(a_1,a_2,a_3,\dots\) be an arithmetic sequence. If \(\frac{a_4}{a_2} = 3\), what is \(\frac{a_5}{a_3}\)?

Lightning  Aug 26, 2018
 #1
avatar+93866 
+3

Let the sequence be

a, a+d, a+2d, a+3d, a+4d

 

\(\frac{a+3d}{a+d}=3 \qquad find \qquad \frac{a+4d}{a+2d}\\ 3a+3d=a+3d\\ 2a=0\\ a=0\\ so\\ \frac{a_5}{a_3}=\frac{a+4d}{a+2d}=\frac{4d}{2d}=2\)

Melody  Aug 26, 2018
 #2
avatar+91027 
+2

Just wanted to try this one, too...

 

a4 / a2   = 3

a4  = 3a2

a4  = a2 + 2d   ...so...

 

a2 + 2d  = 3a2

2d  = 2a2

d  = a2

 

And   a5 /a3  =

 

[ a2 + 3d  ] / [ a2 + d  ] =

 

[d + 3d ] / [ d + d ]

 

4d / 2d  =

 

2

 

This is what Melody got, as well !!!

 

 

cool cool cool

CPhill  Aug 26, 2018
 #3
avatar+803 
+1

Thanks! Both are correct! Thanks for your hard work!

Lightning  Aug 26, 2018

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