When the same constant is added to the numbers 60, 120, and 140, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

 Jun 16, 2024

We can set variables to solve this problem. 

Let's let x be the same constant added to every single number.

The 3 terms in the geometric series must be \(60+x, 120+x, 140+x\)


Since these 3 numbers form a geoemtric series, we can write the equation



Now, we simply solve for x. 

We have \((60+x)(140+x)=(120+x)^2\)


Expanding out everything and combining all like terms, we get




Our geometric series is now \(-90, -30, -10\)

The common ratio is \(-30/-90 = 1/3\)


So our answer is 1/3. 


Thanks! :)

 Jun 16, 2024

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