√3 x √15 = 1.73205080756888 x 3.87298334620742 = 6.70820393249937
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√9x1=3
The geometric mean of two numbers is the square root of their product. In you instance any two factors of 900 will have a geometric mean of 30 eg 2 & 450 (2 x 15 = 30, 30 x 15 = 450); 3 & 300 (3 x 10 = 30, 30 x 10 = 300); 6 & 150 (6 x 5 = 30, 30 x 5 = 150) etc etc
square root of 18
Of sorts. 1 3 6 10 15 would have a geometric representation, but would not fit the definition of a "geometric sequence". One example of a geometric representation of the sequence would be the number of total bowling pins as you add each row. The first row as 1 pin, the second has 2, then 3,4,5. 1 = 1 + 2 = 3 + 3 = 6 + 4 = 10 + 5 = 15
√3 x √300 = 1.73205080756888 x 17.3205080756888 = 30