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The 2nd term of a geometric sequence is 12 and the 5th term is 768. what is the common ratio?

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AGBOIIGO

Answer:

The common ratio is 4

Step-by-step explanation:

Remember that

  • [tex]An = A1r^{n-1}[/tex]

So

  • [tex]A(2) = A1r^{2-1} \: or \: \: \boxed{A1r^1 = 12}[/tex]
  • [tex]A(2) = A1r^{5-1} \: or \: \: \boxed{A1r^4 = 768}[/tex]

Lastly , we eliminate the A1 and solve for the common ratio

[tex] \\ \frac{A1r^4}{ A1r^1} = \frac{768}{12} \\ \\ \frac{ \cancel{A1}r^4}{ \cancel{A1}r^1} = \frac{768}{12} \\ \\ {r}^{3} = 64 \\ \\ r = \sqrt[3]{64} \\ \\ \boxed{ r = 4}[/tex]

GRRRRRLLLLLLLLLLLLLGO

Answer:

r=4

Step-by-step explanation:

n= 5-2 = 3

r =

[tex] \sqrt[n]{ \frac{5th \: term}{2nd \: term} } [/tex]

[tex] \sqrt[3]{ \frac{768}{12} } [/tex]

[tex] \sqrt[3]{64} [/tex]

r = 4

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