Question

Help with arithmetic?

Answer 1

Given the arithmetic sequence a_n = 4 + 8(n – 1), what is the domain for n?

Answer 2

@johnweldon1993 @wio @jdoe0001

Answer 3

Well the domain could be all real numbers, there are no *real* numbers that you can plug in there that would make the sequence invalid

Answer 4

Hm. Okay.

Well the provided choices are...
All integers
All integers where n≥1
All integers where n≥0
All integers where n>1

Answer 5

So it would be all integers :)

Answer 6

Why?

Answer 7

well because...like I said...if you plug any integer in there...you will get an answer...

a_0 = 4 + 8(0 - 1) = -4
a_1 = 4 + 8(1 - 1) = 4
a_2 = 4 + 8(2 - 1) = 12
a_3 = 4 + 8(3 - 1) = 20

etc...there is no stopping the fact that the common difference is 8...and there is no number that you can plug in that would give an answer of like \(\large \infty\) or \(\large -\infty\)

Answer 8

OH got it!

Answer 9

:)

Answer 10

What about a_n=-5+3(n-1)?

Answer 11

@johnweldon1993

Answer 12

It's n≥0, I believe! Thank you!

Answer 13

Why can't it be all real numbers?

Answer 14

Well the common difference is -3

Answer 15

Right

Answer 16

so we have

a_n = -5 + 3(n - 1)

a_0 = -5 + 3(0 - 1) = -5 - 3 = -8

a_1 = -5 + 3(1 - 1) = -5 so we do have a difference of 3

but what about -1?

a_-1 = -5 + 3(-1 - 1) = -5 + 3(-2) = -5 - 6 = -11 so we still have a difference of 3

Answer 17

Uhhh

Answer 18

So n≥1?

Answer 19

No, the example I just wrote had an 'n' of -1 so it doesn't HAVE to be greater than 1

Answer 20

Soo it's n>1?

Answer 21

All integers....remember -1 is also an integer

Answer 22

Shoot.. I'm terrible with this. Thank you so much!

Answer 23

Could you help me with one more?