Geometric progression problem

[PurpleNight]

Hi, so I have this geometric progression task in my homework and I don't know where to start. Any help is appreciated.

3 numbers are elements of a geometric progression. If you divide the first number by 4, subtract 6 from the second number and subtract the sum of the first two from the last number you get again a geometric progression with the same common ratio. What are those numbers?

 

[Deleted member 4993]

Hi, so I have this geometric progression task in my homework and I don't know where to start. Any help is appreciated.

3 numbers are elements of a geometric progression. If you divide the first number by 4, subtract 6 from the second number and subtract the sum of the first two from the last number you get again a geometric progression with the same common ratio. What are those numbers?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Hi, so I have this geometric progression task in my homework and I don't know where to start. Any help is appreciated.

3 numbers are elements of a geometric progression. If you divide the first number by 4, subtract 6 from the second number and subtract the sum of the first two from the last number you get again a geometric progression with the same common ratio. What are those numbers?

Start with what you know about geometric progressions!

If the numbers are x, y, z, what equation(s) can you write to say they form a geometric progression?

One way to do this is to express y and z in terms of x and r, the common ratio.

What are the three numbers you get from x, y, and z, in terms of the three variables (or in terms of x and r)?

What equation(s) can you write to express the condition you are given?

There are many ways to approach this, so we need to see how you choose to start, and whether you make any mistakes as you proceed.

 

[Steven G]

If a is the 1st term of the three and r is the common ratio, then how are these three terms defined.

 

[PurpleNight]

So x,y,z are a,a*r,a*r^2.
x¹,y¹,z¹ are a/4, a*r-6, a*r^2-(a+a*r)

 

[Dr.Peterson]

So x,y,z are a,a*r,a*r^2.
x¹,y¹,z¹ are a/4, a*r-6, a*r^2-(a+a*r)

Good (though I'm not sure how you intend the superscripts to be interpreted).

Now can you write two equations that tell you that these three numbers are also in geometric progression? Solve those two equations for the two variables.

 

[Steven G]

The problem stated 3 numbers are elements of a geometric progression, but did not state that the 3 numbers were consecutive numbers.

I would say that the 1st number is a, the 2nd number is ar^n and the 3rd number is ar^m (assume m>n)

 

[Dr.Peterson]

The problem stated 3 numbers are elements of a geometric progression, but did not state that the 3 numbers were consecutive numbers.

I would say that the 1st number is a, the 2nd number is ar^n and the 3rd number is ar^m (assume m>n)

Can you solve it with that interpretation? You're right that the problem is not stated accurately, but the natural interpretation leads to a simple solution (or two, if you allow negative numbers).

 

[Steven G]

Can you solve it with that interpretation? You're right that the problem is not stated accurately, but the natural interpretation leads to a simple solution (or two, if you allow negative numbers).

I wondered if what I said would lead to an answer, especially since you basically said that the terms are in order.