## anonymous one year ago Find s10 for -1+-7+-13+-19+...

1. SolomonZelman

what pattern do you notice in this sequence?

2. anonymous

the r=-6

3. SolomonZelman

not, exactly. You go down by 6 every time (i.e. subtract 6) BUT the correct notation is d=-6

4. 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)

5. SolomonZelman

You need to find the 10th term first, can you do that for me?

6. SolomonZelman

[[ Use $$\large a_{\rm n}=a_1+{\rm d( n}-1)$$ ]]

7. SolomonZelman

r u lost?

8. anonymous

I got -55?

9. SolomonZelman

Oh, a(10)=-1+(-6)(10-1)=-1+(-6)(9)=-1-54=-55 correct $$a_{10}=-55$$

10. 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: $$\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm n} } A_{\rm n}=\color{red}{\frac{1}{2} \left(a_1+a_{\rm n}\right)}\times \color{blue}{{\rm n}} }$$

11. SolomonZelman

in red I labeled the part of the formula which is the average term. in blue is the number of term

12. SolomonZelman

number of terms*

13. SolomonZelman

well, I should have made the number of terms k... but I will show you how to use this. $$\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm 10} } A_{\rm n}=\color{red}{\frac{1}{2} \left(-1+-55\right)}\times \color{blue}{{\rm 10}} }$$

14. SolomonZelman

in this case.... c y?

15. SolomonZelman

(if you want I can restart in a more handy way, typing isn't a problem.... )

16. anonymous

I got -280 is that right? @SolomonZelman

17. SolomonZelman

no