Question 286343: Find three numbers in geometric progression whose sum is 21 and sum of their squares is 189?
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! Geometric Progression means that the numbers are multiples. For example:
2,4,8 is a geometric progression, because 2x2=4, and then 2x4=8. The next number in the progression would be 8x2=16. The number that you multiply by is called the common ratio. In this case, the common ratio is 2.
For your question, you need to find x, the first number, and r, the common ratio. Let's set up the equations:
Eqn.1: 
Note that the r^2 term comes from multiplying by the common ratio a 2nd time to get the 3rd number.
Eqn. 2: 
I'm not sure what level of math this is. Do you know how to solve equations like this?
I will give you the answer, and hopefully you can work it out. Let me know if you'd like some extra help.
The common ratio, r=2, and the first number x=3.
The three numbers are 3, 6 and 12.
3+6+12=21
3^2+6^2+12^2=9+36+144=189
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