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### Course: Algebra 1>Unit 9

Lesson 6: General sequences

# Sequences and domain

We can generate the same sequence with different functions and different domains. Created by Sal Khan.

## Want to join the conversation?

• I wish he would write the domain definitions using the formal set notation instead of just describing them, since that is what you will see as you advance. It's this kind of laziness that made the higher level maths so confusing because I didn't know any of the notation.
So what is the true, formal, technical way to describe a series and its domain, the way a college professor would write it on the blackboard?
• A(n)=6(2)^n {n∈R|x≥0} I believe
• t(0)=10
t(n)=t(n−1)⋅3

If I have this recursive example and you ask if the domain should be an integer n>=0 or n>= 1 it seems like the answer should be n>=1 because if the domain is n>=0 then in the case where n=0 the first term would be
t(0)=t(0-1)*3
=t(-1)*3 which is the term before zero which is undefined.
I realize t(0) is given to us so the domain must include zero, but the general case then seems to become false. Can anyone help me clarify my thinking?
• The domain would be integers such that n≥0. The recursive formula is good for integers such that n>0.
• Why do messages pop up at and saying that Sal is incorrect? It seems to me that what he is doing is totally legit.
• At , Sal mistakenly said that n is >= than 0. However, in the previous iteration of the expression n is >=1 He made a similar mistake at .
• But if you input the n for the first term in the formula in , won't you get t(n)=2*t(0-1) = 2*t(-1)? Or is the formula just for finding the terms after the first (since the first term is already given)?
• I'm confused because I just took the test and got a question wrong because it said we know something is the domain by what the first term is set as, whether it's 0 or 1. That's not what was shown in this video in the corrections. Is that particular to this sequence?

The question I see is s(1)=24
s(n)=s(n-1)*1/2

It says the domain is greater than or equal to 1 since the first term is defined as 1. I don't understand because if you put it in s(1-1) you get s(0) *1/2.
• I am trying to figure out what you are asking. There is a difference between the domain and the start of n. So in the video, the 0 term is defined (which is part of the domain), but the value of n is an integer such that n≥1. So the domain is integers such that x≥0, but the limitations on n is such that n≥1. I think your problem is the same, the domain would be integers such that x≥1, but the value of n would be defined as integers such that n≥2 (not 1 which is already defined). Does this help your understanding or not?
• How do you solve for domains in which the number get's smaller and smaller?
• It does not change the domain, but it would change the formula. For example, if there was a sequence of 16, 8, 4, 2, 1, 1/2, ,,,,, then the number is being cut in half every time. The formula would be a(n)=16(1/2)^n where n is an integer and n≥0. You could do the same using n-1.
• im so lost am i the only one wh odoesnt know whats happening
• honestly the best way is to just go to the exercise and check out the hints until you get what they want you to do because these videos are a little confusing
• I don't understand this lesson at all, could someone please explain what he is doing and how to solve the exercises?
• honestly the best way is to just go to the exercise and check out the hints until you get what they want you to do because these videos are a little confusing
• If two functions generate the same sequence but have a different domain, are they still considered equivalent?
(1 vote)
• What do you mean by different domains? Most sequences have the domain of n where n is all natural numbers. Occasionally, a sequence will start with the 0 term, so I would assume a sequence that gives the same values for the domain of 1, 2, 3, ... and one included the extra 0 term (which would have to be stated) would be the same sequence.