What is the sixth term in the geometric progression: 27, -3, 1/3?

To determine the sixth term in the geometric progression consisting of the terms 27, -3, and 1/3, we first need to identify the common ratio of the progression. In a geometric series, each term is obtained by multiplying the previous term by a constant called the common ratio.

Let's find the common ratio by dividing the second term by the first term:

-3 / 27 = -1/9.

Next, we can verify this ratio by checking the third term:

1/3 / (-3) = 1/3 * (-1/3) = -1/9.

Since we have confirmed that the common ratio is -1/9, we can use this to find further terms in the geometric progression.

To find the sixth term, we start with the first term (27) and apply the common ratio five times (to get from the first term to the sixth term):

First term = 27

Second term = 27 * (-1/9) = -3

Third term = -3 * (-1/9) = 1/3

Fourth term = 1/3 * (-1/9) = -1/27

Fifth term = -1/27 * (-