Deanna Gregory

2022-09-30

Determine whether the sequence 5,1,0.2,0.04,... is geometric and if it is, what is the common ratio

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Clare Acosta

Expert

$5,1,0.2,0.04\therefore {a}_{1}=5;{a}_{2}=1,{a}_{3}=0.2,{a}_{4}=0.04....$
For Geometric progression $\frac{{a}_{2}}{{a}_{1}}=\frac{{a}_{3}}{{a}_{2}}=\frac{{a}_{4}}{{a}_{3}}=$ constant
Here $\frac{{a}_{2}}{{a}_{1}}=\frac{1}{5}=0.2,\frac{{a}_{3}}{{a}_{2}}=\frac{0.2}{1}=0.2$ ,
$\frac{{a}_{4}}{{a}_{3}}=\frac{0.04}{0.2}=0.2$. This constant (0.2) is called common
ratio. This is geometric progression and common raio is 0.2

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