The third, fifth and seventeenth terms of an arithmetic progression are in geometric progression. Find the common ratio of the geometric progression.

To solve this problem, we need to understand the properties of both arithmetic and geometric progressions.

In an arithmetic progression (AP), the difference between any two successive terms is constant. This difference is called the common difference. If a is the first term of an AP, then the nth term of the AP is given by a + (n-1)d, where d is the common difference.

In a geometric progression (GP), the ratio of any two successive terms is constant. This ratio is called the common ratio.

Given that the third, fifth and seventeenth terms of an arithmetic progression are in geometric progression, we can write the terms of the AP as follows:

Third term, a3 = a + 2d Fifth term, a5 = a + 4d Seventeenth term, a17 = a + 16d

Since these terms form a GP, the ratio of the fifth term to the third term should be equal to the ratio of the seventeenth term to the fifth term. Therefore, we can write the equation as follows:

(a + 4d) / (a + 2d) = (a + 16d) / (a + 4d)

Solving this equation will give us the common ratio of the geometric progression.