Question

Given the following geometric sequence, find the common ratio.

{0.1, -0.9, 8.1, ...}
A. 9
B. -9
C. 1/9
D.-1/9

Answer 1

The common ratio of the geometric sequence {0.1, -0.9, 8.1, ...} is -9, as calculated by dividing the second term by the first term.

Step-by-step explanation:

The student has asked to find the common ratio of the given geometric sequence {0.1, -0.9, 8.1, ...}. To calculate the common ratio (r), we can divide any term by the preceding term in the sequence. Dividing the second term (-0.9) by the first term (0.1), we get:

r = -0.9 / 0.1 = -9

Thus, the common ratio of the geometric sequence is -9, which corresponds to option B. We can double-check this by multiplying the second term by the common ratio to see if we get the third term:

-0.9 * -9 = 8.1

This confirms that the common ratio is indeed -9.