Question

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

-8 - 3 + 2 + 7 + ... + 67
PLEASEEEE

Answer 1

@amistre64 @mathstudent55 do u know this by any chance??

Answer 2

yes

Answer 3

awesome! how would I go about doing this?

Answer 4

lets assume since the values are pretty close to one another that the sequence is arithmetic; what defines an arithmetic sequence?

Answer 5

arithmetic sequence has consecutive terms that are increasing or decreasing at a consistent rate?

Answer 6

correct, or simply, there is some constant value being added each time

-8 + k = -3
-3 + k = 2
2 + k = 7

does this look like itll fit for some k? and if so, what would the value of k be?

Answer 7

k=5 :D

Answer 8

good, then lets follow this out

a0 = -8
a1 = -8 + 5
a2 = -8 + 5 + 5
a3 = -8 + 5 + 5 + 5
a4 = -8 + 5 + 5 + 5 + 5

an = -8 + 5n , for n=0 to whatever

do you agree?

Answer 9

sometimes its easier to work with when n starts at 1 instead of 0, to adjust for that we just subtract 1 from n

an = -8 + 5(n-1) , for n=1 to whatever
= -13 + 5n

Answer 10

ahhhh okay yes I understand that part! now how do I determine if it goes to infinity or just a set number of times like 15?

Answer 11

well, we know that it has to end at some n such that the rule equals 67:

67 = -13 + 5n; for n=1 to ??

Answer 12

I meant what I am seeing in my answers is \[\sum_{n=0}^{15}(-8+5n) and \sum_{n=0}^{oo}(-8+5n)\]

Answer 13

ahh, well we know that n=infinity gets huge .... and -8+5(huge) is way to big to be 67 right?

what does -8 +5(15) equal?

Answer 14

67 so I guess it has to go to infinity right?

Answer 15

-8 - 3 + 2 + 7 + ... + 67
^^^
as a rule of thumb, of you have an end to
your sequence of numbers .... you just cant
have an infinite set.

Answer 16

it cant go into infinity .... it has a stopping point

Answer 17

ahh okay so then it stops at 67??

Answer 18

when n= 0: -8+5(0) = - 8
when n=15: -8+5(15) = 67

so n has to go from 0 to 15 to fit the problem

Answer 19

yes, it stops at: +67

Answer 20

that makes sense, so in any arithmetic sequence they can not go to infinity?

Answer 21

depends on problem

spose it just ended it at: -8,-3,2,7,...

the three dots at the end there are notation for going on and on and on and on .... to infinity

Answer 22

but, yours tells us that it starts at -8, goes on a ways following some rule, then stops at 67

Answer 23

AHHH NOW I UNDERSTAND!!! derp that was a dumb mistake I made

Answer 24

Thank you so much

Answer 25

youre welcome