Question

Classify each sequence as arithmetic, geometric, or neither by dragging it into the correct box.

Answer 1

The sequences are classified, respectively, as:

Geometric, Arithmetic, Neither.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

In the first sequence, we have that:

$q = \frac{45}{15} = \frac{15}{5} = \frac{5}{\frac{5}{3}} = \frac{\frac{5}{3}}{\frac{5}{9}} = 3$

Hence it is a geometric sequence.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

In the second sequence, we have that:

d = -4 - 1 = 1 - 6 = 6 - 11 = 11 - 16 = -5

Hence it is an arithmetic sequence.

What about the third sequence?

$\frac{4}{3} \neq \frac{3}{2}, 1 - \frac{1}{2} \neq 2 - 1$

Hence it is neither arithmetic nor geometric.

More can be learned about geometric and arithmetic sequences at brainly.com/question/11847927

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