Determine the common ratio r of an increasing geometric progression, for which the first term is 5 and the third term is 20.Choices:- 2 -2 -4 10

In a geometric progression, the ratio between any term and the previous term is constant. This is called the common ratio.

Given that the first term (a) is 5 and the third term is 20, we can use the formula for the nth term of a geometric progression to find the common ratio (r).

The formula is: a_n = a * r^(n-1)

We know that a = 5, n = 3 (because we're looking for the third term), and a_n = 20.

So we can set up the equation:

20 = 5 * r^(3-1)

Solving for r, we get:

20 = 5 * r^2

Divide both sides by 5:

4 = r^2

Take the square root of both sides:

r = ±2

So the common ratio could be either 2 or -2.

Looking at the choices given, both 2 and -2 are options. However, the problem specifies that the geometric progression is increasing. This means that each term must be larger than the previous term. Therefore, the common ratio must be positive.

So the answer is 2.