Question

Identify the sequence as arithmetic, geometric, or neither. Explain your answer.

Answer 1

Answer:

It's a geometric sequence

Step-by-step explanation:

$\text{If}\ a_1,\ a_2,\ a_3,\ ....\ \text{is}\\\\(1)\ \text{an arithmetic sequence, then}\\a_2-a_1=a_3-a_2=a_4-a_3=...=a_n-a_{n-1}=d=constant\\\\(2)\ \text{a geometric sequence, then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=r=constant$

$\text{We have}\\\\1.6,\ 0.8,\ 0.4,\ 0.2,\ ...\\\\\text{check the difference:}\\\\0.8-1.6=-0.8\\0.4-0.8=-0.4\\\\\text{different differences}\\\\\bold{CONCLUSION}\\\text{It's not an arithmetic sequence}\\\\\text{check the quotient:}\\\\\dfrac{0.8}{1.6}=\dfrac{8}{16}=\dfrac{1}{2}\\\\\dfrac{0.4}{0.8}=\dfrac{4}{8}=\dfrac{1}{2}\\\\\dfrac{0.2}{0.4}=\dfrac{2}{4}=\dfrac{1}{2}\\\\\text{the same quotient}\\\\\bold{CONCLUSION}\\\text{It's a geometric sequence with common ratio}\ r=\dfrac{1}{2}=0.5$