Question

drag each tile to the correct box.

three geometric sequences are given below.

sequence a: \\(160, 40, 10, 2.5, \dots\\)
sequence b: \\(-21, 63, -189, 567, \dots\\)
sequence c: \\(8, 12, 18, 27, \dots\\)

order the sequences from least common ratio to greatest common ratio.

Explanation:

⚡ Using what you learned: Geometric Sequences

Step 1: Find the common ratio of Sequence A

$$ r_A = \frac{40}{160} = \frac{1}{4} = 0.25 $$

Step 2: Find the common ratio of Sequence B

$$ r_B = \frac{63}{-21} = -3 $$

Step 3: Find the common ratio of Sequence C

$$ r_C = \frac{12}{8} = \frac{3}{2} = 1.5 $$

Step 4: Order the common ratios from least to greatest

$$ -3 < 0.25 < 1.5 $$

$$ r_B < r_A < r_C $$

Answer:

The correct order from least common ratio to greatest common ratio is:

Sequence B, Sequence A, Sequence C