Find the 9th term of the geometric progression (аn) if а1 = 64 and q = 1/2

Note that the terms of the geometric progression are denoted by bn, not an.

As we know, any member of such a progression is calculated by the formula bn = b1 * q ^ (n – 1).

Let us determine which number will be in ninth place in our geometric progression, if from the condition of the task we know that the first number that is included in this progression is 64, while its denominator is 1/2:

b9 = 64 * 1/2 ^ (9 – 1) = 2 ^ 6 * 1/2 ^ 8 = 1/2 ^ 2 = 1/4.

Answer: Under such initial conditions, the ninth term of the progression will be 1/4.