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# Pls help me thank you!!!

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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
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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!

Mar 30, 2020
#2
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thx man and I love my name to XD

Mar 30, 2020