Question

for each sequence, determine whether it appears to be arithmeti
4, 8, 16, 32, ...
arithmetic
geometric
neither
1000, 100, 10, 1, ...
arithmetic
geometric
neither
4, 8, 12, 16, ...
arithmetic
geometric
neither

Explanation:

Step1: Check 4,8,16,32,... for arithmetic

Compute differences: $8-4=4$, $16-8=8$, $32-16=16$. Differences are not constant.

Step2: Check 4,8,16,32,... for geometric

Compute ratios: $\frac{8}{4}=2$, $\frac{16}{8}=2$, $\frac{32}{16}=2$. Ratios are constant.

Step3: Check 1000,100,10,1,... for arithmetic

Compute differences: $100-1000=-900$, $10-100=-90$, $1-10=-9$. Differences are not constant.

Step4: Check 1000,100,10,1,... for geometric

Compute ratios: $\frac{100}{1000}=0.1$, $\frac{10}{100}=0.1$, $\frac{1}{10}=0.1$. Ratios are constant.

Step5: Check 4,8,12,16,... for arithmetic

Compute differences: $8-4=4$, $12-8=4$, $16-12=4$. Differences are constant.

Step6: Check 4,8,12,16,... for geometric

Compute ratios: $\frac{8}{4}=2$, $\frac{12}{8}=1.5$, $\frac{16}{12}=\frac{4}{3}$. Ratios are not constant.

Answer:

• 4, 8, 16, 32, ...: Geometric
• 1000, 100, 10, 1, ...: Geometric
• 4, 8, 12, 16, ...: Arithmetic