Question

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

Answer 1

what pattern do you notice in this sequence?

Answer 2

the r=-6

Answer 3

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

Answer 4

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)

Answer 5

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

Answer 6

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

Answer 7

r u lost?

Answer 8

I got -55?

Answer 9

Oh,
a(10)=-1+(-6)(10-1)=-1+(-6)(9)=-1-54=-55

correct \(a_{10}=-55\)

Answer 10

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:

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

Answer 11

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

Answer 12

number of terms*

Answer 13

well, I should have made the number of terms k... but I will show you how to use this.

\(\large\color{black}{ \displaystyle \sum_{ {\rm n}=1 }^{ {\rm 10} } A_{\rm n}=\color{red}{\frac{1}{2} \left(-1+-55\right)}\times \color{blue}{{\rm 10}} }\)

Answer 14

in this case.... c y?

Answer 15

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

Answer 16

I got -280 is that right? @SolomonZelman

Answer 17

no