Question

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

-1 + 2 + 5 + 8 + ... + 44 PLEASE HELP, THANKS!

Answer 1

Find the formula for the sequence first

Answer 2

Okay, let me work on that.

Answer 3

I am at a loss right now, I really do not understand how to go about this problem. Could you walk me through it, if you are willing?

Answer 4

Find the common difference first

Answer 5

d=3

Answer 6

Find the difference between the common difference and the first term

Answer 7

as in 3-(-1)= 4?

Answer 8

Yep

Answer 9

Therefore \(\Large a_n=-3n+4\)

Answer 10

What does n equal when:
(1) \(a_n=-1\)?
(2) \(a_n=44\)?

Answer 11

(1) n= 7
(2) n= -128
?

Answer 12

You reversed them, I'm asking the opposite

Answer 13

I apologize if I am wrong; I am sincerely confused when it comes to these problems. I will try again.

Answer 14

You thought I gave you values of n and you found a_n, where in fact I gave you values of a_n and you find n

Answer 15

So would I set up equations as follows? :
(1) -1=-3n+4
(2) 44=-3n+4

Answer 16

Yep

Answer 17

Because you have the formula of the sequence

Answer 18

You want to know where it starts and where it ends

Answer 19

-1 is the start and 44 is the end

Answer 20

Oh, I see my mistake. So then we have the values:
(1) 5/3
(2) -(40/3)

I do understand the start and ending points though.

Answer 21

Or do I actually not solve out the equations and I am making a fool of myself?

Answer 22

Wait my bad it should be \(\Large a_n=3n+4\) and yes you do solve the equation

Answer 23

You want to know which n corresponds to -1 (the first term) and which n corresponds to 44 (the last term)

Answer 24

And you aren't making a fool of yourself

Answer 25

(Thank you holding in here with me; it's greatly appreciated.)
(1) -(5/3) and this would correspond to the first term, correct?
(2) 40/3 and this would correspond to the second term?

Answer 26

Please solve the equations again

Answer 27

Because of my bad I modified the equationd

Answer 28

I'll explain the significance later

Answer 29

(1) -1= 3n+4
(2) 44= 3n+4
Wouldn't their answers be the same as before, but just have opposite signs?

Answer 30

Sorry my bad again... It should be \(a_n=3n-4\)

Answer 31

Oh, and it's okay.
(1) -1= 3n-4
= 1
(2) 44= 3n-4
= 16

Answer 32

Therefore when n=1, a_n=-1
When n=16, a_n=44

Answer 33

Therefore the 1st term is -1 and the 16th term is 44

Answer 34

Therefore it's \(\displaystyle\Large\sum_{n=1}^{16}(3n-4)\)

Answer 35

This makes perfect sense! I understand the process of writing out eh summation notation, thank you! There's just one problem; these are the only answer choices:
\[\sum_{n=0}^{15}-3n\]
\[\sum_{n=0}^{15}(-1+3n)\]
\[\sum_{n=0}^{\infty}-3n\]
\[\sum_{n=0}^{\infty}(-1+3n)\]

Answer 36

Oh that's just the same

Answer 37

\[\sum_{n=1}^{16}(3n-4)=\sum_{n=0}^{15}(3n-1)\]

Answer 38

Oh, I was worried there for a bit. Thank you so much for your help; you have been of great service to me! Thanks a ton!!

Answer 39

No problem