Find s10 for -1+-7+-13+-19+...

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Find s10 for -1+-7+-13+-19+...

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what pattern do you notice in this sequence?
the r=-6
not, exactly. You go down by 6 every time (i.e. subtract 6) BUT the correct notation is d=-6

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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)
You need to find the 10th term first, can you do that for me?
[[ Use \(\large a_{\rm n}=a_1+{\rm d( n}-1) \) ]]
r u lost?
I got -55?
Oh, a(10)=-1+(-6)(10-1)=-1+(-6)(9)=-1-54=-55 correct \(a_{10}=-55\)
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: \(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm n} } A_{\rm n}=\color{red}{\frac{1}{2} \left(a_1+a_{\rm n}\right)}\times \color{blue}{{\rm n}} }\)
in red I labeled the part of the formula which is the average term. in blue is the number of term
number of terms*
well, I should have made the number of terms k... but I will show you how to use this. \(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm 10} } A_{\rm n}=\color{red}{\frac{1}{2} \left(-1+-55\right)}\times \color{blue}{{\rm 10}} }\)
in this case.... c y?
(if you want I can restart in a more handy way, typing isn't a problem.... )
I got -280 is that right? @SolomonZelman
no

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