Answer: The answer is either 4, 12, 36 or 100, 60, 36.
Step-by-step explanation: Let the first two numbers be 'a' and 'b'.
According to the question, a, b and 36 forms a geometric series. So, we have
![\dfrac{b}{a}=\dfrac{36}{b}\\\\\Rightarrow b^2=36a.](https://tex.z-dn.net/?f=%5Cdfrac%7Bb%7D%7Ba%7D%3D%5Cdfrac%7B36%7D%7Bb%7D%5C%5C%5C%5C%5CRightarrow%20b%5E2%3D36a.)
Also, if 36 is replaced by 20, then a, b, 20 will form an arithmetic series. So,
![b-a=20-b\\\\\Rightarrow 2b=20+a\\\\\Rightarrow 2b=20+\dfrac{b^2}{36}\\\\\Rightarrow 72b=720+b^2\\\\\Rightarrow b^2-72b+720\\\\\Rightarrow b^2-60b-12b+720=0\\\\\Rightarrow b(b-60)-12(b-60)=0\\\\\Rightarrow (b-12)(b-60)\\\\\Rightarrow b=12,~~b=60.](https://tex.z-dn.net/?f=b-a%3D20-b%5C%5C%5C%5C%5CRightarrow%202b%3D20%2Ba%5C%5C%5C%5C%5CRightarrow%202b%3D20%2B%5Cdfrac%7Bb%5E2%7D%7B36%7D%5C%5C%5C%5C%5CRightarrow%2072b%3D720%2Bb%5E2%5C%5C%5C%5C%5CRightarrow%20b%5E2-72b%2B720%5C%5C%5C%5C%5CRightarrow%20b%5E2-60b-12b%2B720%3D0%5C%5C%5C%5C%5CRightarrow%20b%28b-60%29-12%28b-60%29%3D0%5C%5C%5C%5C%5CRightarrow%20%28b-12%29%28b-60%29%5C%5C%5C%5C%5CRightarrow%20b%3D12%2C~~b%3D60.)
Therefore,
![a=\dfrac{12^2}{36}=4,~~a=\dfrac{60^2}{36}=100.](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B12%5E2%7D%7B36%7D%3D4%2C~~a%3D%5Cdfrac%7B60%5E2%7D%7B36%7D%3D100.)
Thus, the three numbers are either 4, 12, 36 or 100, 60, 36.