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When the same constant is added to the numbers 60, 120, and 160, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

 Jun 15, 2024

Best Answer 

 #1
avatar+1952 
+1

Let's set variables in order to solve this problems.

Let's let c be the constant added to each number. 

 

We get 60+c,120+c,160+c

 

Since all the terms form an geometric series, we can write the formula

60+c120+c=120+c160+c

 

Now, we simplfy solve for c. 

(c+160)(60+c)=(c+120)(120+c)

 

Distributing everything, combining all like terms, and moving everything to one side, we get

20c4800=0

c=240

 

We plug this back in, and we get the series 180,120,80

 

This has a common ratio of 180/120=3/2

 

So 3/2 is our answer, 

 

Thanks! :)

 Jun 15, 2024
 #1
avatar+1952 
+1
Best Answer

Let's set variables in order to solve this problems.

Let's let c be the constant added to each number. 

 

We get 60+c,120+c,160+c

 

Since all the terms form an geometric series, we can write the formula

60+c120+c=120+c160+c

 

Now, we simplfy solve for c. 

(c+160)(60+c)=(c+120)(120+c)

 

Distributing everything, combining all like terms, and moving everything to one side, we get

20c4800=0

c=240

 

We plug this back in, and we get the series 180,120,80

 

This has a common ratio of 180/120=3/2

 

So 3/2 is our answer, 

 

Thanks! :)

NotThatSmart Jun 15, 2024

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