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katiebugg

  • 3 years ago

The sum of a geometric series is -2044. If the first term is -4 and the common ratio is 2, what is the final term in the sequence?

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  1. Yahoo!
    • 3 years ago
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    Sn = a[r^n-1]/r-1

  2. Yahoo!
    • 3 years ago
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    use this and find n

  3. waterineyes
    • 3 years ago
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    Wait @Yahoo!

  4. Yahoo!
    • 3 years ago
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    then an = a*r^(n-1)

  5. Yahoo!
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    Why @waterineyes any mistake

  6. waterineyes
    • 3 years ago
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    Sorry my mistake... Ha ha ha..

  7. Yahoo!
    • 3 years ago
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    \[-2044 = -4[2^n -1]/(2-1)\]

  8. Yahoo!
    • 3 years ago
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    511 = 2^n - 1 510 = 2^n

  9. Yahoo!
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    find n??

  10. rsadhvika
    • 3 years ago
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    \(-2044 = -4. \frac{2^{n}-1}{2-1}\) \(-2044 = -4. (2^{n}-1)\) \(511 = 2^{n}-1\) \(512 = 2^{n}\) \(2^9 = 2^{n}\) 9=n

  11. waterineyes
    • 3 years ago
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    512

  12. Yahoo!
    • 3 years ago
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    sorry 512 = 2^n

  13. Yahoo!
    • 3 years ago
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    now n = 9

  14. Yahoo!
    • 3 years ago
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    subs in an = a * r^(n-1)

  15. waterineyes
    • 3 years ago
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    \[\large 2^n = 512 \implies 2^n = 2^9 \implies \color{green}{n = 9}\]

  16. Yahoo!
    • 3 years ago
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    an = -4 * 2^8

  17. waterineyes
    • 3 years ago
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    you can replace n here by 9 @Yahoo!

  18. Yahoo!
    • 3 years ago
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    256 * -4 = -1024

  19. katiebugg
    • 3 years ago
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    lol thanks!

  20. Yahoo!
    • 3 years ago
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    Welcome

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