Respuesta :

let [tex]a_n[/tex] be the n'th term of the sequence.

so [tex]a_1[/tex] is the first term, [tex]a_2[/tex] the second term and so on...

In a geometric sequence with [tex]a_1=c[/tex], and common ratio r, the terms are as follows:

[tex]a_1=c[/tex]
[tex]a_2=cr[/tex]
[tex]a_3=c r^{2} [/tex]
[tex]a_4=c r^{3} [/tex]
.
.
that is, each term is its previous term times the common ratio r.

In our example

[tex]a_2=cr=20[/tex] and [tex]a_4=c r^{3}=11.25 [/tex]

[tex] \frac{a_2}{a_4}= \frac{cr}{c r^{3}}= \frac{1}{ r^{2}}= \frac{20}{11.25}= 1.778 [/tex]

so [tex]r^{2} =1/1.778=0.56[/tex]

[tex]r= \sqrt{0.56}= 0.75[/tex]


Answer: r=0.75

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