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anonymous

  • one year ago

What is the sum of a 7-term geometric series if the first term is −6, the last term is −24,576, and the common ratio is −4?

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  1. PhantomCrow
    • one year ago
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    Do you know the formula?

  2. anonymous
    • one year ago
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    nope...

  3. anonymous
    • one year ago
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    @Deadly_Roses

  4. PhantomCrow
    • one year ago
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    The formula for the sum of a geo series is:\[S _{n}=\frac{ a _{1} (1-r^n)}{ 1-r }\]

  5. anonymous
    • one year ago
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    would it be -34,766?

  6. PhantomCrow
    • one year ago
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    That's not what I got. n=7 r=-4

  7. PhantomCrow
    • one year ago
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    So\[S _{n}=-6(1-(-4)^7/1-(-4)\]

  8. anonymous
    • one year ago
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    is the fraction bar localized to 14^7/1, or does it encompass everything in parenthesis?

  9. PhantomCrow
    • one year ago
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    everything

  10. anonymous
    • one year ago
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    im fried...

  11. PhantomCrow
    • one year ago
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    Alright.\[S _{n}=\frac{ -6(1-(-4)^7) }{ 1-(-4)}\] This further simplifies to\[S_{n}=\frac{ -6(1-(-16834)) }{ 5 }\] Simplify again...\[S_{n}=\frac{ -6(1+16834) }{ 5 }\]\[S_{n}=\frac{ -98310 }{ 5 }\]\[S_{n}=-19662\]

  12. anonymous
    • one year ago
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    mind blown 0.0

  13. PhantomCrow
    • one year ago
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    Haha. As long as you know the series formulas, you should be good to go for any type of these problems.

  14. anonymous
    • one year ago
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    alright. im gonna leave this open so i can write down the formula when i come back on Wednesday. thank you for your time and help

  15. PhantomCrow
    • one year ago
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    No problem.

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