Question

1. which sequence has a common ratio of 2?

(20, 15, 10, 5, 0, -5, ...)
(20, 4, 0.80, 0.16, 0.032, 0.0064, ...)
(20, 40, 80, 160, 320, 640, ...)
(20, 10, 5, 2.5, 1.25, 0.625, ...)

Explanation:

⚡ Using what you learned: Geometric Sequences

Step 1: Define common ratio

The common ratio \( r \) of a geometric sequence is found by dividing any term by its preceding term:

$$ r = \frac{a_{n}}{a_{n-1}} $$

Step 2: Test the options

• Option 1: \(\{20, 15, 10, 5, 0, -5, ...\}\)

$$ \frac{15}{20} = 0.75 \quad (\text{This is an arithmetic sequence with } d = -5) $$

• Option 2: \(\{20, 4, 0.80, 0.16, 0.032, 0.0064, ...\}\)

$$ \frac{4}{20} = 0.2 $$

• Option 3: \(\{20, 40, 80, 160, 320, 640, ...\}\)

$$ \frac{40}{20} = 2 $$

$$ \frac{80}{40} = 2 $$

• Option 4: \(\{20, 10, 5, 2.5, 1.25, 0.625, ...\}\)

$$ \frac{10}{20} = 0.5 $$

Answer:

The sequence with a common ratio of 2 is:
\(\{20, 40, 80, 160, 320, 640, ...\}\) (the third option)