The geometric progression is given by its first term b1 = 256 and the denominator q = 1/2.

The geometric progression is given by its first term b1 = 256 and the denominator q = 1/2. Find the ninth term of this progression.

Solution.

Formula of the n-th term of a geometric progression.

bn = b1 q n-1.

Let’s substitute in this formula the values of the first term and the denominator of the geometric progression.

bn = 256 (1/2) n-1.

For the ninth term n = 9, we get

b9 = 256 (1/2) 8 = 256: 28 = 256: 256 = 1.

Answer. The ninth term of the geometric progression is 1.