5. The numbers x, 17/12 and y are the first three terms of an arithmetic progression. The numbers x, 2/3 and y are three consecutive terms of a geometric progression. Determine the values of x and y.

Step-by-step explanation:

The numbers x, and y are the first three terms of an arithmetic progression.

For three consecutive terms, a, b and c of an arithmetic sequence:

The arithmetic mean,

Therefore:

The numbers x, and y are three consecutive terms of a geometric progression.

For three consecutive terms, a, b and c of a geometric sequence:

The geometric mean,

Therefore:

Substituting derived above, we have:

This is a quadratic equation which we can then solve for y.

Using a calculator, we obtain:

Therefore, the values of x and y are:

none cuz there are no "following statements" regarding the question

step-by-step explanation: