Precalculus: Represent the sequence -3, 1, 5, 9, 13, 17, 21 using sigma notation.

[Sarahsally]

My son and I are currently working on his Precalculus math homework. We are both incredibly stuck.

"Represent the sequences using sigma notation in at least two different representations.
1. -3, 1, 5, 9, 13, 17, 21."

Any help would be appreciated, thanks!

 

[Sarahsally]

Precalculus Homework Help

I have been doing pretty well with Sigma notation, but then I got to one question on a quiz that absolutely stumped me.
"Represent the sequences using sigma notation in at least two different representations.

1. -3, 1, 5, 9, 13, 17, 21."

My understanding of Sigma leads me to believe that the numbers plugged into the equation must be consecutive, but I haven't found any consecutive numbers that lead to the sequence above.

 

[Deleted member 4993]

My son and I are currently working on his Precalculus math homework. We are both incredibly stuck.

"Represent the sequences using sigma notation in at least two different representations.
1. -3, 1, 5, 9, 13, 17, 21."

Any help would be appreciated, thanks!

What is "sigma notation" for sequences?

 

[Sarahsally]

What is "sigma notation" for sequences?

Thats what we were wondering. If there isn't one, then maybe the teacher made a typo. (She hasn't been the best)

 

[Deleted member 4993]

Thats what we were wondering. If there isn't one, then maybe the teacher made a typo. (She hasn't been the best)

What does your text-book say?

 

[Bob Brown MSEE]

If sequence is partial sums then...

nth partial sum is given by,

\(\displaystyle \text{-7 + }


\sum _{k=1}^n 4\)

 

[Sarahsally]

What does your text-book say?

He is currently taking an online class and there is no textbook provided. He does have some notes but this was definitely not in it.

 

[Deleted member 4993]

He is currently taking an online class and there is no textbook provided. He does have some notes but this was definitely not in it.

In that case, a search (e.g. through Google) of the key-word would be advised.

By the way, your son should ask for help directly.

 

[stapel]

My son and I are currently working on his Precalculus math homework. We are both incredibly stuck.

"Represent the sequences using sigma notation in at least two different representations.
1. -3, 1, 5, 9, 13, 17, 21."

What does your text-book say?

He is currently taking an online class and there is no textbook provided. He does have some notes but this was definitely not in it.

Then your son may need to have a serious talk with the department, letting them know that the class is being tested over material which their instructor has not covered. This is irresponsible, and possibly fraud.

Many of us have learned, from hard experience, that attempting to "speak" through a "translator" who doesn't "know the language" is doomed to end badly. So your son then also needs to do some online research, since it is not reasonably feasible to attempt to (1) figure out what all may have been skipped in the "classroom" and then (2) replace the missing hours of lecture content. He can get started with lessons like this, and use Google to find loads more lessons.

Once he has studied at least two lessons, please have him attempt the exercise. If he gets stuck, please have him reply with a clear listing of his thoughts and efforts so far, at which point we can begin to work with him. Thank you!

 

[Bob Brown MSEE]

another way

nth partial sum is given by,

\(\displaystyle \text{-7 + 4}


\sum _{k=1}^n 1\)



Note that

\(\displaystyle \text{n = }

\sum _{k=1}^n 1\)

and

Sn = 4n-7

 

[Ishuda]

My son and I are currently working on his Precalculus math homework. We are both incredibly stuck.

"Represent the sequences using sigma notation in at least two different representations.
1. -3, 1, 5, 9, 13, 17, 21."

Any help would be appreciated, thanks!

First 'Sigma notation' as I understand it: The capital sigma stands for sum, i.e.
\(\displaystyle \Sigma_1^n\, a_n\, =\, a_1\, +\,a_2\, +\,a_3\, ...\, +\,a_n\)

So, lets look at the sequence from the standpoint of Sigma notation
\(\displaystyle \Sigma_1^1\, a_n\, =\, -3\)
\(\displaystyle \Sigma_1^2\, a_n\, =\,\, 1\)
\(\displaystyle \Sigma_1^3\, a_n\, =\,\, 5\)
\(\displaystyle \Sigma_1^4\, a_n\, =\,\, 9\)
\(\displaystyle \Sigma_1^5\, a_n\, =\, 13\)
\(\displaystyle \Sigma_1^6\, a_n\, =\, 17\)
\(\displaystyle \Sigma_1^7\, a_n\, =\, 21\)
...
Given the above what is a₁? Now we have
\(\displaystyle \Sigma_1^{n+1}\, a_n\, -\, \Sigma_1^n\, a_n\, =\, a_{n+1}\)
Let n=1. So what is a₂? Let n=2. What is a₃? Let n=3. What is a₄? ... Do you see a pattern?