anonymous
  • anonymous
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?
Mathematics
katieb
  • katieb
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PhantomCrow
  • PhantomCrow
Do you know the formula?
anonymous
  • anonymous
nope...
anonymous
  • anonymous

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PhantomCrow
  • PhantomCrow
The formula for the sum of a geo series is:\[S _{n}=\frac{ a _{1} (1-r^n)}{ 1-r }\]
anonymous
  • anonymous
would it be -34,766?
PhantomCrow
  • PhantomCrow
That's not what I got. n=7 r=-4
PhantomCrow
  • PhantomCrow
So\[S _{n}=-6(1-(-4)^7/1-(-4)\]
anonymous
  • anonymous
is the fraction bar localized to 14^7/1, or does it encompass everything in parenthesis?
PhantomCrow
  • PhantomCrow
everything
anonymous
  • anonymous
im fried...
PhantomCrow
  • PhantomCrow
Alright.\[S _{n}=\frac{ -6(1-(-4)^7) }{ 1-(-4)}\] This further simplifies to\[S_{n}=\frac{ -6(1-(-16834)) }{ 5 }\] Simplify again...\[S_{n}=\frac{ -6(1+16834) }{ 5 }\]\[S_{n}=\frac{ -98310 }{ 5 }\]\[S_{n}=-19662\]
anonymous
  • anonymous
mind blown 0.0
PhantomCrow
  • PhantomCrow
Haha. As long as you know the series formulas, you should be good to go for any type of these problems.
anonymous
  • anonymous
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
PhantomCrow
  • PhantomCrow
No problem.

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