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Let \(a_1,a_2,a_3,...\)be an arithmetic sequence. If \((a_4)/(a_2)=3\), what is \(a_5/a_3\)

 Mar 30, 2020
 #1
avatar+626 
+1

Hello BIGChungus!  I like your name!
 

Plan:

For arithmetic problems, I like using variables.

 

First term = x

Common difference = y

 

We can define an arithmetic sequence this way:

 

x + (x + y) + (x + 2y) + (x + 3y)....

Set up and solve:

(1) \(\frac{a_4}{a_2}=\frac{x+3y}{x+y}=3\)

 

(2) \(\frac{a_5}{a_3}=\frac{x+4y}{x+2y}=?\)

 

Let us get rid of the fraction in (1) by multiplying both sides by (x+y)

x + 3y = 3x + 3y

-2x = 0

x = 0

 

Wow! The first term is 0.

 

Let us plug that into (2).

\(\frac{0+4y}{0+2y}\)

 

Simplify

\(\frac{4y}{2y}=2\)

 

Ta-da! Mathz! cheeky

 Mar 30, 2020
 #2
avatar+148 
0

thx man and I love my name to XD

 Mar 30, 2020

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