Question

Write the sum using summation notation, assuming the suggested pattern continues.

-10 - 2 + 6 + 14 + ... + 110

Answer 1

your sequence is an arithmetic sequence with constant d= 8

Answer 2

first term is:
\[{a_1} = - 10\]

Answer 3

ok i understand that

Answer 4

n-th term is:
\[{a_n} = 110\]

Answer 5

what is n?

Answer 6

or, in other words how many terms have you got in your sequence?

Answer 7

5 terms?

Answer 8

so n is equal to 5

Answer 9

I don't think, you have to apply this formula:
\[{a_n} = {a_1} + (n - 1) \cdot d\]
where d= 8, a_1 = -10, and a_n = 110, so please solve that equation for n

Answer 10

ok one sec

Answer 11

hint:
\[n - 1 = \frac{{{a_n} - {a_1}}}{d} = \frac{{110 - \left( { - 10} \right)}}{8} = ...?\]

Answer 12

15 :D

Answer 13

please wait you got:
n-1 = 15 so what is n?

Answer 14

14

Answer 15

just find the pattern, and put it in the \(\large\color{blueviolet}{ \displaystyle \sum_{ }^{ } ~}\)

Answer 16

yes, find whichTH term 110 is, and do the sigma

Answer 17

hint:
if n-1 = 15, then
n = 15+1=...?

Answer 18

if anyone needs the latex for inline sigma, then
```
\(\large\color{blueviolet}{ \displaystyle \sum_{ n=1 }^{ \infty } ~ f(n)}\)
```

Answer 19

N=16

Answer 20

that's right! so in you sequence there are 16 terms

Answer 21

Ok!

Answer 22

now, in order to get the sum S of tose terms, you have to apply this formula:
\[S = \frac{{{a_1} + {a_n}}}{2}n\]

Answer 23

oops.. those terms...

Answer 24

hint:
\[S = \frac{{{a_1} + {a_n}}}{2}n = \frac{{ - 10 + 110}}{2} \cdot 16 = ...?\]

Answer 25

800...?

Answer 26

well done! Congratulations! :)

Answer 27

:D

Answer 28

Is that it...?

Answer 29

yes! it is!

Answer 30

But it doesn't match any of the answers given 0.0

Answer 31

The answers have the "E"

Answer 32

I can't make it on this key board :/

Answer 33

please wait I think that @SolomonZelman is right! since we have to write in the sum notation

Answer 34

Ok :)

Answer 35

so our result, since there are infinite terms is:
\[\sum\limits_1^\infty {{a_1} + \left( {n - 1} \right)} \,d\]

Answer 36

S there are no longer 16 terms...?

Answer 37

please you have to substitute a_1 and d with our numerical values

Answer 38

A1=-10 d=8

Answer 39

no I don't think, since your problem says "assuming that the pattern"

Answer 40

ok! sbstitute a_1 = -10 andd = 8, into this formula
\[\sum\limits_1^\infty {{a_1} + \left( {n - 1} \right)} \,d\]

Answer 41

Ahh ok

Answer 42

So what do I put for n?

Answer 43

E(-10)+(8n-8)

Answer 44

please unchanged n, write n without any substitution for it

Answer 45

yes! now simplify like terms, namely what is:
-10+8n-8=...?

Answer 46

?

Answer 47

So (n-8)?

Answer 48

you should get this:
\[\sum\limits_1^\infty {8n - 18} \]

Answer 49

-18

Answer 50

since -10 + 8n - 8= 8n-18

Answer 51

no, 8n-18

Answer 52

I am on an I pad so sorry if everything is taking forever to load if for you

Answer 53

please we have:
(-10)+(8n-8)= 8n-18

Answer 54

+ 8n

Answer 55

-18 + 8n

Answer 56

(-10)+(8n-8) = -10 + 8n -8 = -10 - 8 +8n = -18 + 8n

Answer 57

That still doesn't match any of my answers T.T

Answer 58

it is a simplification, since I have combined similar terms

Answer 59

E=-80n
E=(-10+8n)

Answer 60

Tose are the answer choices

Answer 61

and the result is:
\[\sum\limits_1^\infty {8n - 18} \]

Answer 62

those done match any of my answer options

Answer 63

please is it clear?

Answer 64

E=-80n
or E=(-10+8n)

Answer 65

if not I will give you more explanation

Answer 66

are you still there? ;-;

Answer 67

wait you lost me ; ;

Answer 68

the answer we got doesnt match any of the answer choices

Answer 69

ok! I'm here!

Answer 70

please what are your choices?

Answer 71

ok the answer choices are either E=-80n or E= (-10+8n)

Answer 72

then it is the second option

Answer 73

ok and there are two of the "second" option
on has a 15 over the E and the other has an infinity symbol over it

Answer 74

please wait, are you reading them from your textbook?

Answer 75

no

Answer 76

this is from an assignment the teacher gave us

Answer 77

then you have to pick the one which has an infinity symbol

Answer 78

ok thanks :DDD

Answer 79

thanks! :)