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anonymous

  • one year ago

The following is a geometric sequence. -1/2, 1/4, -1/8, 1/16

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  1. anonymous
    • one year ago
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    @Loser66

  2. anonymous
    • one year ago
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    idk im confuessed

  3. Michele_Laino
    • one year ago
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    hint: the ratio between one term and its preceding term is constant, and we can write this: \[\left( {1/16} \right):\left( { - 1/8} \right) = \left( { - 1/8} \right):\left( {1/4} \right) = \left( {1/4} \right):\left( { - 1/2} \right) = ...?\]

  4. anonymous
    • one year ago
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    still lost.

  5. Michele_Laino
    • one year ago
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    hint: \[\frac{1}{{16}}:\left( { - \frac{1}{8}} \right) = \frac{1}{{16}} \times \left( { - 8} \right) = ...\]

  6. anonymous
    • one year ago
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    i do.. and @Michele_Laino is it -1/2?

  7. Michele_Laino
    • one year ago
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    yes! that's right!

  8. anonymous
    • one year ago
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    so i mutliply each by -1/2?

  9. Michele_Laino
    • one year ago
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    yes you have to multiply one term by -1/2 in order to get the subsequent term of your geometric sequence

  10. anonymous
    • one year ago
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    so its only a geometric sequence if its multiply by a fraction?

  11. Michele_Laino
    • one year ago
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    no, the constant can be also an integer number, or even a irrational number

  12. anonymous
    • one year ago
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    so is something like -5,0,5,10 a geometric sequence?

  13. Michele_Laino
    • one year ago
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    no, it is an arithmetic sequence, since the difference between one term and its preceding term is constant: 0-(-5)= 5-0= 10-5=...?

  14. anonymous
    • one year ago
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    okay! but what if its like -5,25,-125,625 when its all multiply by -5

  15. Michele_Laino
    • one year ago
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    it is a geometric sequence whose constant is -5

  16. anonymous
    • one year ago
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    but why?

  17. Michele_Laino
    • one year ago
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    because the ration between one term and its preceding term is a constant value

  18. Michele_Laino
    • one year ago
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    ratio*

  19. anonymous
    • one year ago
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    okay i get it

  20. Michele_Laino
    • one year ago
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    ok!

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