6. Determine if the sequence is arithmetic or geometric, and the common ratio or
difference.
-4,-2.5, -1, 0.5, 2,
A. Arithmetic; d = 1.5
B. Arithmetic; d = 2
C. Geometric; r = 0.5
D. Geometric; r = 2

A. Arithmetic; d = 1.5

Step-by-step explanation:

-4, -2.5, -1, 0.5, 2

Looking at the sequence, we can see that the numbers increase. This means our common ration or difference will be positive.

Let's look at common ratios first.

To find the common ratio, divide one term from the term after it.

r = a₂ ÷ a₁

r = -2.5 / -4

Divide.

r = 0.625

To see if this is the common ratio, we want to test this with the other numbers of the sequence.

r = a₃ ÷ a₂

r = -1 / -2.5

r = 0.4

This is not consistent; therefore our sequence is not geometric.

Let's look at common differences next.

To find the common ratio, subtract one term from the term after it.

r = a₂ - a₁

r = -2.5 - (-4)

Simplify.

r = -2.5 + 4

Add.

r = 1.5

To see if this is the common difference, we want to test this with the other numbers of the sequence.

r = a₃ - a₂

r = -1 - (-2.5)

Simplify.

r = -1 + 2.5

r = 1.5

This is consistent; therefore we have found our common difference of this arithmetic sequence.

A. Arithmetic; d = 1.5

Hope this helps!

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32