Geometric Progression

The geometric mean of numbers is given by the formula: where are the numbers. For the numbers 10, 16, and 50, the geometric mean is: First, calculate the product: Now, calculate the cube root: Thus, the geometric mean of 10, 16, and 50 is 20.

We are given the sequence: We can observe that each term is being multiplied by 3 to get the next term: Therefore, the next term will be: Thus, the next term in the sequence is .

The geometric mean (G.M.) of three numbers is given by the formula: Substitute the given values :