Find the number of members of a geometric progression in which the first, second and last terms

Find the number of members of a geometric progression in which the first, second and last terms are 3.12 and 3072, respectively?

In order to find the number of members of a geometric progression, we use the formula for the nth term of a geometric progression.

bn = b1 * q ^ (n – 1);

Let’s write the formula for the second term of the progression and substitute the values of the terms:

b2 = b1 * q;

12 = 3 * q;

q = 4.

Once again, we write the formula for the nth term and substitute other values:

bn = b1 * q ^ (n – 1);

3072 = 3 * 4 ^ (n – 1);

1024 = 4 ^ (n – 1);

4 ^ 5 = 4 ^ (n – 1);

We equate the exponents:

5 = n – 1;

n = 6.

Answer: There are exponentially 6 members.