Question

select the sequences that are geometric.
□ 18, 36, 54, 72, ...
□ 4.1, 8.2, 16.4, 32.8, ...
□ -7, 14, -28, 56, ...
□ 980, 784, 627.2, 501.76, ...
□ 5, 2, -1, -4, ...
done

Explanation:

Step1: Recall Geometric Sequence Definition

A geometric sequence has a common ratio \( r \), where \( r=\frac{a_{n + 1}}{a_n} \) for all \( n \). We check each sequence:

Step2: Check Sequence 1: 18, 36, 54, 72,...

Calculate ratios: \( \frac{36}{18}=2 \), \( \frac{54}{36}=1.5 \), \( \frac{72}{54}\approx1.333 \). Ratios are not equal. Not geometric.

Step3: Check Sequence 2: 4.1, 8.2, 16.4, 32.8,...

Ratios: \( \frac{8.2}{4.1}=2 \), \( \frac{16.4}{8.2}=2 \), \( \frac{32.8}{16.4}=2 \). Common ratio \( r = 2 \). Geometric.

Step4: Check Sequence 3: -7, 14, -28, 56,...

Ratios: \( \frac{14}{-7}=-2 \), \( \frac{-28}{14}=-2 \), \( \frac{56}{-28}=-2 \). Common ratio \( r=-2 \). Geometric.

Step5: Check Sequence 4: 980, 784, 627.2, 501.76,...

Ratios: \( \frac{784}{980}=0.8 \), \( \frac{627.2}{784}=0.8 \), \( \frac{501.76}{627.2}=0.8 \). Common ratio \( r = 0.8 \). Geometric.

Step6: Check Sequence 5: 5, 2, -1, -4,...

Ratios: \( \frac{2}{5}=0.4 \), \( \frac{-1}{2}=-0.5 \). Ratios not equal. Not geometric.

Answer:

• 4.1, 8.2, 16.4, 32.8, ...
• -7, 14, -28, 56, ...
• 980, 784, 627.2, 501.76, ...