anonymous
  • anonymous
The following is a geometric sequence. -1/2, 1/4, -1/8, 1/16
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@Loser66
anonymous
  • anonymous
idk im confuessed
Michele_Laino
  • Michele_Laino
hint: the ratio between one term and its preceding term is constant, and we can write this: \[\left( {1/16} \right):\left( { - 1/8} \right) = \left( { - 1/8} \right):\left( {1/4} \right) = \left( {1/4} \right):\left( { - 1/2} \right) = ...?\]

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anonymous
  • anonymous
still lost.
Michele_Laino
  • Michele_Laino
hint: \[\frac{1}{{16}}:\left( { - \frac{1}{8}} \right) = \frac{1}{{16}} \times \left( { - 8} \right) = ...\]
anonymous
  • anonymous
i do.. and @Michele_Laino is it -1/2?
Michele_Laino
  • Michele_Laino
yes! that's right!
anonymous
  • anonymous
so i mutliply each by -1/2?
Michele_Laino
  • Michele_Laino
yes you have to multiply one term by -1/2 in order to get the subsequent term of your geometric sequence
anonymous
  • anonymous
so its only a geometric sequence if its multiply by a fraction?
Michele_Laino
  • Michele_Laino
no, the constant can be also an integer number, or even a irrational number
anonymous
  • anonymous
so is something like -5,0,5,10 a geometric sequence?
Michele_Laino
  • Michele_Laino
no, it is an arithmetic sequence, since the difference between one term and its preceding term is constant: 0-(-5)= 5-0= 10-5=...?
anonymous
  • anonymous
okay! but what if its like -5,25,-125,625 when its all multiply by -5
Michele_Laino
  • Michele_Laino
it is a geometric sequence whose constant is -5
anonymous
  • anonymous
but why?
Michele_Laino
  • Michele_Laino
because the ration between one term and its preceding term is a constant value
Michele_Laino
  • Michele_Laino
ratio*
anonymous
  • anonymous
okay i get it
Michele_Laino
  • Michele_Laino
ok!

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