Question

what is the 5th partial sum of
infinity
*sigma notation* -3+5n
n=1

Answer 1

Answer choices:
55
60
65
70

Please expain it too, cause I would like to know how to do another one

Answer 2

1st term, plug in 1 to -3+5n and get 2
2nd term put in two and get 7 ....
5ith term put in 5
add them all up.

Answer 3

how high would I go though? Cause it says infinity

Answer 4

2+7+12+17+22= 60

Answer 5

5 terms

Answer 6

the series is defined for infinity but when they ask for the nth partial they only want the first n terms

Answer 7

ohh so if they want the 5th partial sum, you add up the first 5 terms?

Answer 8

i simpler way to write that would be

sum (1 to inf) of: -3+5n

Answer 9

I dont think it is phrazed right, its the 5th partial sum of sumation blah blah from to infinity

Answer 10

correct mother

Answer 11

its really sum (1 to 5) of: -3+5n

Answer 12

does the rule define a sequence that then gets partially sumed?

Answer 13

\[\sum_{1}^{5} -3+5n\]

Answer 14

so wait say in this problem:

\[\sum_{8}^{n=5}\]

Answer 15

yeah I think so but Im just saying the computation is like 1->5

Answer 16

a (with a sub-note) of n next to sigma notation

Answer 17

\[\sum_{1}^{5} -3+5n\]
\[\sum_{1}^{5} -3+\sum_{1}^{5} 5n\]
\[ -3\sum_{1}^{5}+5\sum_{1}^{5}n\]

Answer 18

8->5 does not make any sense

Answer 19

hold on. my computer is going slow so when it was loading it switched the numbers

Answer 20

but even if you go "backwards" you will get the same thing so...

Answer 21

8
sigma notation a (sub-note) n
n=5

Answer 22

thats it^ my computer wasnt loading right.

Answer 23

how do you put that in a calculator?

Answer 24

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Answer 25

\[\sum_{5}^{8}-3+2n\] = (-3+2(5))+(-3+2(6))+(-3+2(7))+(-3+2(8))

Answer 26

no theres a(n) next to the sigma notation. But the n is like below it

Answer 27

same thing

Answer 28

yeah same thing

Answer 29

the way you wrote is the better notation...

Answer 30

but how you put that in a calculator?

Answer 31

causse the n is below it

Answer 32

depends on the calculator

Answer 33

for ti89 i think its sigma(-3+2n, n, 5, 8)

Answer 34

is there anyway to do it online?

Answer 35

the n is jsut telling you the variable name so like
\[\sum_{n=1}^{8}3x\] would not make sense to talk about.

Answer 36

but wait theres 2 variables a and n. Im sorry Im completely confused on this one

Answer 37

A is the function name
A(n) = A_n = -3+2n for natural numbers n
this is the notation we use to show we are talking about n as integers and not real numbers

Answer 38

there is a way to do it online

if you type

sum(-3+5n,n=1..5)

into wolfram alpha, you'll get \[\Large \sum_{n=1}^{5} -3+5n = 60\]


wolfram alpha: www.wolframalpha.com

Answer 39

of course, this should be a way to check your work (and not do it completely for you)

Answer 40

also get to know the such that key | on your calculator, it will make life easy

Answer 41

thankyou! can you help me with the one below

Answer 42

Im just really confused on that one still

Answer 43

\[\Large \sum_{n=5}^{8} a_{n}\]

literally means "add the terms a5, a6, a7, a8"

So

\[\Large \sum_{n=5}^{8} a_{n} = a_{5}+a_{6}+a_{7}+a_{8}\]


The only problem is that I don't know what \(\Large a_{n}\) is (is it \(\Large a_{n} = -3+5n\) ?)

Answer 44

ohh cause my answer choices are
54
102
144
162

Answer 45

what is the sequence \(\Large a_{n}\) in this case? You didn't specify

Answer 46

-3,0,3

Answer 47

so it looks like you're adding 3 each time

Answer 48

those are the first three terms, what are the next 5 terms?

Answer 49

6, 9, 12, 15, 18,

Answer 50

Now list the 5th, 6th, 7th, and 8th terms

Answer 51

18, 21, 24, 27

Answer 52

Sorry, I should have stated that the first 8 terms are...


-3, 0, 3, 6, 9, 12, 15, 18


This is of course assuming that -3, 0, 3 are the first three terms (that are given)

Answer 53

right

Answer 54

so the 5th, 6th, 7th, and 8th terms of the sequence

-3, 0, 3, 6, 9, 12, 15, 18

are...???

Answer 55

21,24,27,30

Answer 56

no

Answer 57

they're in that list somewhere

Answer 58

sorry that wasnt the 5th, 6th 7th. I didnt read that part

Answer 59

thats ok

Answer 60

9, 12, 15, 18

Answer 61

now add those terms up

Answer 62

54

Answer 63

thats the answer?!

Answer 64

good, so...


\[\Large \sum_{n=5}^{8} a_{n} = a_{5}+a_{6}+a_{7}+a_{8}\]


\[\Large \sum_{n=5}^{8} a_{n} = 9+12+15+18\]


\[\Large \sum_{n=5}^{8} a_{n} = 54\]

Answer 65

it is

Answer 66

thankyou SO much!

Answer 67

you're welcome