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.