Question

Is the the sequence `5a-1, 3a-1, a-2, -a-1,...` arithmetic?

Answer 1

Interpretation 1: Assuming the question is with `a- 2`:

The common difference, `d`, of a sequence will determine whether it is arithmetic, geometric or neither. If it is arithmetic, the common difference will be a common number added or subtracted from the previous term.

`d = t_2 - t_1`

`d = 3a - 1 - (5a - 1)`

`d = 3a - 1 - 5a + 1`

`d = -2a`

`d= t_3 - t_2`

`d = a - 2 - (3a - 1)`

`d = -2a - 1`

Since the two numbers aren't the same, this sequence is not arithmetic

Interpretation 2: Assuming the question is with `a - 1`

Doing the same process as above:

`d = t_2 - t_1`

`d = 3a - 1 - (5a - 1)`

`d = 3a - 1 - 5a + 1`

`d = -2a`

`d = t_3 - t_2`

`d = a - 1 -(3a - 1)`

`d = a - 1 - 3a + 1`

`d = -2a`

Since the two `d's` are the same, this sequence is arithmetic.

Hopefully this helps!