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iheartfood

  • 2 years ago

In a geometric sequence, the term an+1 can be smaller than the term an. true or false?

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  1. irkiz
    • 2 years ago
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    true

  2. irkiz
    • 2 years ago
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    if n is < 1

  3. iheartfood
    • 2 years ago
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    are u sure?? how did u know so fast?? lol

  4. irkiz
    • 2 years ago
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    as in |n| < 1

  5. irkiz
    • 2 years ago
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    so n ranges from 0 to 1

  6. irkiz
    • 2 years ago
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    oops

  7. irkiz
    • 2 years ago
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    wait

  8. iheartfood
    • 2 years ago
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    oh okay

  9. irkiz
    • 2 years ago
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    if the interval is (-1) that makes it alternating

  10. irkiz
    • 2 years ago
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    so it will be smaller and bigger alternatingly

  11. irkiz
    • 2 years ago
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    (-1)^ 2 is positive, (-2) ^ 3 is negative

  12. iheartfood
    • 2 years ago
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    so this is FALSE?

  13. irkiz
    • 2 years ago
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    (-2)^2 i mean

  14. campbell_st
    • 2 years ago
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    if the common ratio r <1 then each term is smaller that the previous

  15. irkiz
    • 2 years ago
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    there are a few cases yeah. if the sequence convergerges or if the sign alternates

  16. iheartfood
    • 2 years ago
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    wait so its TRUE then???

  17. irkiz
    • 2 years ago
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    yup its true

  18. irkiz
    • 2 years ago
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    i said wait coz my explanation was incomplete

  19. iheartfood
    • 2 years ago
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    oh okay haha :P thanks!!! so its definitely TRUE right?

  20. campbell_st
    • 2 years ago
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    if the absolute value of r is less than 1 |r| < 1 the the geometric series will have a limiting sum...

  21. campbell_st
    • 2 years ago
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    just to clarify things... n is used for the term number... and r is used for the common ratio ( or multiplication constant)... just to avoid confusion.

  22. iheartfood
    • 2 years ago
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    k thanks for all the help y'all!

  23. irkiz
    • 2 years ago
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    yeah. \[ar ^{n}\] if |r| < 1 it converges and if r is negative, it alternates

  24. campbell_st
    • 2 years ago
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    not quite a term in a geometric series is found using \[T_{n} = ar^{n -1}\] n is the term number, T is the Term a is the 1st term and r is the common ratio... please get it right @irkiz

  25. iheartfood
    • 2 years ago
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    k thanks for all the help y'all!

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