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?
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
−20c−4800=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! :)
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
−20c−4800=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! :)