The geometric progression (an) is given by the formula an = 3 * 2 ^ n. find the number of the sequence

The geometric progression (an) is given by the formula an = 3 * 2 ^ n. find the number of the sequence term equal to 384.

First of all, we note that in order to determine the ordinal number of a member of a geometric progression, it is necessary to equate the formula given in the condition of this task to the number corresponding to our member of the progression. Hence, we get the following equation:

3 * 2 ^ n = 384.

Divide both sides of the equation by 3:

3 * 2 ^ n = 384 | : 3;

2 ^ n = 384: 3;

2 ^ n = 128.

Let’s represent the right side of the equation as a power of 2:

2 ^ n = 128;

2 ^ n = 2 7.

Then n = 7.

Answer: 384 is the 7th term in the progression.