Question

Help with arithmetic sequences?

Answer 1

What is the domain for n in \[a_{n}=4-3(n-1)\]

Answer 2

options ?

Answer 3

All Integerswhere n ≥ 1
All integers where n > 1
All Integerswhere n ≤ 4
All Integerswhere n ≥ 4

Answer 4

well, n is the number of the term, correct?

Answer 5

Yess

Answer 6

so, can you have a 1st term?

Answer 7

Yes?

Answer 8

ok, and you can also have
2nd, 3rd, 4th terms and on....

but not 4.6th term.

Answer 9

so what can you tell me about the n ?

Answer 10

I'm really sorry but I'm not sure.

Answer 11

ok, can you have 1/2th term ?

Answer 12

No

Answer 13

@SolomonZelman

Answer 14

Yes, so the number of a term has to be a whole number (as that you can't have 1/4th term - same way as you can't have 1/4 of a friend), and a positive number (you can't have negative second term, just like you can't have negative 2 phones on your table).

Answer 15

And "integer" means any whole positive or negative number.
like
.... -4 , -3 , -2, -1, 0, 1, 2, 3, 4 ....

Answer 16

Ohh right!

Answer 17

When you say that this integer is more than or equal to 1, all you mean is that your possible numbers are

1, 2, 3, 4, 5, .....

Answer 18

if you said all integers greater than 1, than it would be same as above but without the 1.

Such that: 2, 3, 4, 5, .....

Answer 19

and if \(n\ge 4\)
that would mean that n can be
4, 5, 6, 7, ....

Answer 20

and lastly if \(n>4\)
then you have all possible n values as follows:
5, 6, 7, 8, .....

Answer 21

OH I understand! Thank you so much!

Answer 22

Wait no I don't.

Answer 23

How do I determine the domain?

Answer 24

@satellite73 @jim_thompson5910

Answer 25

@tkhunny

Answer 26

The domain for sequences is the set of natural numbers (which is why N or n is commonly used)

natural numbers are also called counting numbers

it's basically the set {1, 2, 3, 4, 5, 6, 7, ...}

http://www.mathwords.com/n/natural_numbers.htm

Note: 0 is not included in the natural number set. If you want 0 included, then you refer to the set of whole numbers [0, 1, 2, 3, 4, ...}

Answer 27

Okay, then how do I know which set will work?

Answer 28

@jim_thompson5910

Answer 29

how would you write {1, 2, 3, 4, 5, 6, 7, ...} as an inequality?

Answer 30

n < 1

Answer 31

nope

Answer 32

n < 1 will have things like 0, -1, -2, etc

Answer 33

OH then n > 1?

Answer 34

closer

Answer 35

n > 1 leaves out n = 1

Answer 36

n ≥ 1

Answer 37

correct

Answer 38

Okay so how do I apply this? I'm really stuck.

Answer 39

what do you mean?

Answer 40

I have no idea how to solve this using the information you provided.

Answer 41

can I see the full problem as a screenshot?

Answer 42

so you already have your answer, \(\Large n \ge 1\)

I don't know where you're stuck at

Answer 43

How did I get that?

Answer 44

because n can be replaced with any of these numbers from this set

{1, 2, 3, 4, 5, 6, 7, ...}

Answer 45

How do we know those numbers work?

Answer 46

because n = 1 is always the first term

if you started at n = 0, then you'd have to make a note like "n = 3 is actually the fourth term" but that's confusing. n = 4 is a better way of saying "that's the fourth term"

Answer 47

well I mean "n = 1" is what you plug in to get the first term

Answer 48

OH I understand! Thank you so much!

Answer 49

np