Question

Is the following an arithmetic sequence? 5, 0, -5, -10,...
Yes or No

Answer 1

if there is a common difference between the terms, then it is.

Answer 2

is
0-5 = -5-0 = -10-(-5) ??

Answer 3

Common difference meaning that when subtracting each one, they result in the same difference.

Answer 4

ok so what do I subtract it by?

Answer 5

Well, we go backwards.

Answer 6

-10 -(-5)
-5 - 0
0 - 5

Do they all have the same difference?

Answer 7

Well, let's see.

-10 -(-5)

-(- always cancels out to and addition so:

-10 + 5 = ?
-10 + 5 = -5

Now, if this is an arithmetic sequence we have to prove that the rest of the difference are equal to -5.

Answer 8

So, for it to be an arithmetic sequence:

-5 - 0 must be proven to be -5

0 - 5 must be proven to be -5

-5 - 0 = ?

-5 - 0 = -5

0 - 5 = ?

0 - 5 = -5

-5
-5
-5

Now can we say this is an arithmetic sequence?

Answer 9

Yes

Answer 10

There you go :3