Question

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form.18,6,2,…

Answer 1

• Geometric Sequence.

,

• Common ratio = 1/3

Explanation:

Before we begin, a little background:

• An ,arithmetic sequence, is a sequence in which the next term is derived by the ,addition of a constant, to the previous term. The constant added is called the ,common difference,.

,

• A ,geometric sequence, is a sequence in which the next term is derived by the ,multiplication ,of the previous term by a constant. The constant is called the ,common ratio,.

Given the sequence:

`18,6,2,\cdots`

Divide the next term by the previous term:

`\begin{gathered} (6)/(18)=(1)/(3) \\ (2)/(6)=(1)/(3) \end{gathered}`

We see that the next term is derived by multiplying the next term by 1/3.

Therefore:

• The sequence is a geometric sequence.

,

• The common ratio is 1/3.