omargomez8948 omargomez8948
  • 23-05-2020
  • Mathematics
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Determine the common ratio and find the next four terms of the geometric sequence. a^-6, a^-2, a^2

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TheLazyNobita
TheLazyNobita TheLazyNobita
  • 23-05-2020

Answer:

[tex]a = a^{-6} \\ a_1 = a^{-2 }\\ a_3 = a^2[/tex]

Common ratio(r) = [tex]\displaystyle\frac{a_2}{a_1}[/tex]

[tex]r = \displaystyle\frac{a^{-2}}{a^{-6}}[/tex]

[tex]r = a^4[/tex]

Next 4 terms :

[tex]a_4 = ar^3 = a^{-6 }× a^12 = a^6[/tex]

[tex]a_5 = ar^4 = a^{-6} × a^16 = a^10[/tex]

[tex]a_6 = ar^5 = a^{-6} × a^20 = a^14[/tex]

[tex]a_7 = ar^6 = a^{-6} × a^24 = a^18[/tex]

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