Question

determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
108, 18, 3, ...
answer attempt 1 out of 3
this is
an arithmetic
a geometric
sequence and the
is equal to
.

Explanation:

Step1: Check for arithmetic sequence

Calculate the difference between consecutive terms: $18 - 108 = -90$ and $3 - 18 = -15$. Since the differences are not equal, it is not an arithmetic sequence.

Step2: Check for geometric sequence

Calculate the ratio between consecutive terms: $\frac{18}{108} = \frac{1}{6}$ and $\frac{3}{18} = \frac{1}{6}$. Since the ratios are equal, it is a geometric sequence with a common ratio of $\frac{1}{6}$.

Answer:

This is a geometric sequence and the common ratio is equal to $\frac{1}{6}$.