anonymous
  • anonymous
Find s10 for -1+-7+-13+-19+...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
what pattern do you notice in this sequence?
anonymous
  • anonymous
the r=-6
SolomonZelman
  • SolomonZelman
not, exactly. You go down by 6 every time (i.e. subtract 6) BUT the correct notation is d=-6

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SolomonZelman
  • SolomonZelman
when you say d=-6 that would mean you subtract -6, if you say r=-6 that would mean you are multiplying times -6 d = common difference (adding) r = common ratio (multiplying)
SolomonZelman
  • SolomonZelman
You need to find the 10th term first, can you do that for me?
SolomonZelman
  • SolomonZelman
[[ Use \(\large a_{\rm n}=a_1+{\rm d( n}-1) \) ]]
SolomonZelman
  • SolomonZelman
r u lost?
anonymous
  • anonymous
I got -55?
SolomonZelman
  • SolomonZelman
Oh, a(10)=-1+(-6)(10-1)=-1+(-6)(9)=-1-54=-55 correct \(a_{10}=-55\)
SolomonZelman
  • SolomonZelman
Now, (when you start from \(a_1\) and end the series at \(a_n\) (provided this series is arithmetic, which it is in this case) the sum, for n terms is given the following way: \(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm n} } A_{\rm n}=\color{red}{\frac{1}{2} \left(a_1+a_{\rm n}\right)}\times \color{blue}{{\rm n}} }\)
SolomonZelman
  • SolomonZelman
in red I labeled the part of the formula which is the average term. in blue is the number of term
SolomonZelman
  • SolomonZelman
number of terms*
SolomonZelman
  • SolomonZelman
well, I should have made the number of terms k... but I will show you how to use this. \(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm 10} } A_{\rm n}=\color{red}{\frac{1}{2} \left(-1+-55\right)}\times \color{blue}{{\rm 10}} }\)
SolomonZelman
  • SolomonZelman
in this case.... c y?
SolomonZelman
  • SolomonZelman
(if you want I can restart in a more handy way, typing isn't a problem.... )
anonymous
  • anonymous
I got -280 is that right? @SolomonZelman
SolomonZelman
  • SolomonZelman
no

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