Question

Arithmetic, Geometric, or Neither Classify each sequence as arithmetic, geometric, or neither. (matching) 4/9, 4/3, 4, 12, 36. 0, 1, 2, 3, 4, 5, 6. -10, -6, -2, 2, 6, 10.

Answer 1

Answer:

The given sequence is neither arithmetic not geometric.

Step-by-step explanation:

A sequence is in arithmetic if it has a common difference.

i.e., a sequence a, b, c is in arithmetic if

b - a = c - b

Let's check if the given sequence is in arithmetic.

$\frac{4}{3} -\frac{4}{9} =\frac{12}{9} -\frac{4}{9}$

$= \frac{8}{9}$

$4-\frac{4}{3} =\frac{12-4}{3}$

$=\frac{8}{3}$

So, $\frac{4}{3} -\frac{4}{9} \neq 4-\frac{4}{3}$

Hence, the given sequence is not arithmetic.

Let's check if the given sequence is in geometric.

A sequence is in geometric if it has a common ratio.

i.e., a sequence a, b, c is in geometric if

$\frac{b}{a} =\frac{c}{b}$

$\frac{4/3}{4/9} =\frac{4}{3} (\frac{9}{4} )$

= 3

$\frac{4}{4/3} =4(\frac{3}{4} )$

= 3

Clearly, $\frac{12}{4} =\frac{36}{12} =3$

But, $\frac{0}{36} =0$

Therefore, the given sequence is not in geometric.

Hence, the given sequence is neither arithmetic not geometric.